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FNV Hash

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FNV quick index



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FNV hash history

The basis of the FNV hash algorithm was taken from an idea sent as reviewer comments to the IEEE POSIX P1003.2 committee by Glenn Fowler and Phong Vo back in 1991. In a subsequent ballot round: Landon Curt Noll improved on 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 hashes are designed to be fast while maintaining a low collision rate. The FNV speed allows one to quickly hash lots of data while maintaining a reasonable collision rate. The high dispersion of the FNV hashes makes them well suited for hashing nearly identical strings such as URLs, hostnames, filenames, text, IP addresses, etc.

The IETF has an informational draft on The FNV Non-Cryptographic Hash Algorithm

The FNV hash is in wide spread use:

  • calc
  • Domain Name Servers
  • mdbm key/value data lookup functions
  • Database indexing hashes
  • major web search / indexing engines
  • high performance EMail servers
  • Netnews history file Message-ID lookup functions
  • Anti-spam filters
  • NFS implementations (e.g., FreeBSD 4.3, IRIX, Linux (NFS v4))
  • Cohesia MASS project server collision avoidance
  • spellchecker programmed in Ada 95
  • flatassembler's open source x86 assembler - user-defined symbol hashtree
  • PowerBASIC inline assembly routine
  • text based referenced resources for video games on the PS2, Gamecube and XBOX
  • non-cryptographic file fingerprints
  • FRET - a tool to identify file data structures / helps to understand file formats
  • used to in the process of computing Unique IDs in DASM (DTN Applications for Symbian Mobile-phones)
  • Used by Microsoft in their hash_map implementation for VC++ 2005
  • Used in an implementation of libketama for use in items such as memcache.
  • Used in the realpath cache in PHP 5.x (php-5.2.3/TSRM/tsrm_virtual_cwd.c).
  • Used to improve the fragment cache at twitter (see slide 31).
  • Used in the BSD IDE project
  • Used in the deliantra game server for it's shared string implementation
  • Used to improve Leprechaun, an extremely fast word list creator
  • Favored as a hash for IPv6 Flow Labels in a University of Auckland Computer Science Technical Report (2012-002) of March 2012
  • Used in the speed-sensitive guts of twistylists, an open-source structured namespace manager

FNV hash algorithms and source code have been released into the public domain. The authors of the FNV algorithmm took deliberate steps to disclose the algorhtm in a public forum soon after it was invented. More than a year passed after this public disclosure and the authors deliberatly 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 as published.

If you use an FNV function in an application, why not tell tells us about it by sending EMail to:

fnv EMail addr

There is no requirement to tell us. But if you do, we will be happy to add your application to the above list.

Comments are welcome.


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The core of the FNV hash

The core of the FNV-1 hash algorithm is as follows:

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

The offset_basis and FNV_prime can be found in the parameters of the FNV-1/FNV-1a hash section below.

NOTE: We recommend that you use the FNV-1a alternative algorithm instead of the FNV-1 hash where possible.


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FNV-1a alternate algorithm

There is a minor variation of the FNV hash algorithm known as FNV-1a:

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

The only difference between the FNV-1a hash and the FNV-1 hash is the order of the xor and multiply. The FNV-1a hash uses the same FNV_prime and offset_basis as the FNV-1 hash of the same n-bit size.

The offset_basis and FNV_prime can be found in the parameters of the FNV-1/FNV-1a hash section below.

Some people use FNV-1a instead of FNV-1 because they see slightly better dispersion for tiny (<4 octets) chunks of memory.

One person reported that the FNV-1 hash was not as good as the FNV-1a hash, for their purpuses, because the final octet is not as well dispersed. They reported that the FNV-1a hash was better for error detection, for example.

Other people report that either FNV-1 or FNV-1a make a fine hash. (Try it with with just a dash of Sage and ground Cloves :-))

NOTE: We recommend that you use the FNV-1a alternative algorithm instead of the FNV-1 hash where possible.


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

The FNV-1 hash parameters are as follows:

  • hash is an n bit unsigned integer, where n is the bit length of hash.

  • The multiplication is performed modulo 2n where n is the bit length of hash.

  • The xor is performed on the low order octet (8 bits) of hash.

  • The FNV_prime is dependent on n, the size of the hash:

    32 bit FNV_prime = 224 + 28 + 0x93 = 16777619

    64 bit FNV_prime = 240 + 28 + 0xb3 = 1099511628211

    128 bit FNV_prime = 288 + 28 + 0x3b = 309485009821345068724781371

    256 bit FNV_prime = 2168 + 28 + 0x63 = 374144419156711147060143317175368453031918731002211

    512 bit FNV_prime = 2344 + 28 + 0x57 =
    35835915874844867368919076489095108449946327955754392558399825615420669938882575
    126094039892345713852759


    1024 bit FNV_prime = 2680 + 28 + 0x8d =
    50164565101131186554345988110352789550307653454047907443030175238311120551081474
    51509157692220295382716162651878526895249385292291816524375083746691371804094271
    873160484737966720260389217684476157468082573

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

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

    32 bit offset_basis = 2166136261

    64 bit offset_basis = 14695981039346656037

    128 bit offset_basis = 144066263297769815596495629667062367629

    256 bit offset_basis =
    100029257958052580907070968620625704837092796014241193945225284501741471925557


    512 bit offset_basis =
    96593031294966694980094354007163104660904187456726378961083743294344626579945829
    32197716438449813051892206539805784495328239340083876191928701583869517785


    1024 bit offset_basis =
    14197795064947621068722070641403218320880622795441933960878474914617582723252296
    73230371772215086409652120235554936562817466910857181476047101507614802975596980
    40773201576924585630032153049571501574036444603635505054127112859663616102678680
    82893823963790439336411086884584107735010676915

    NOTE: Older versions of this web page incorretly indicated that the 128 bit FNV_prime was 2168 + 28 + 0x59. This was not correct. While that satisfied all of the significant FNV_prime properties, it was not the smallest 128 bit FNV_prime. The 128 bit offset_basis changed from 275519064689413815358837431229664493455 to 144066263297769815596495629667062367629 was changed as a result of the 128 bit FNV_prime correction. (Sorry about that!)

    These non-zero integers are the FNV-0 hashes of the following 32 octets:

    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> /\\../\\"

    Regarding the offset_basis value:

    The switch from FNV-0 to FNV-1 was purely to change the offset_basis to a non-zero value. The selection of that non-zero value is arbitrary. The string:

    chongo <Landon Curt Noll> /\../\
    was used because the tester was looking at an EMail message from Landon in Landon's standard EMail signature line. Actually the person who did that did not see very well. Landon, today, uses ()'s instead of <>'s and his ASCII bats use "oo" eyes instead of ".." as in:

    chongo (Landon Curt Noll) /\oo/\
    We didn't bother correcting her error because it does not matter. In the general case, almost any offset_basis will serve so long as it is non-zero.

    The following calc script was used to compute the offset_basis for FNV-1 hashes:

    hash_bits = insert_the_hash_size_in_bits_here;
    FNV_prime = insert_the_FNV_prime_here;
    offset_basis = 0;
    offset_str = "chongo <Landon Curt Noll> /\\../\\";
    hash_mod = 2^hash_bits;
    
    str_len = strlen(offset_str);
    for (i=1; i <= str_len; ++i) {
        offset_basis = (offset_basis * FNV_prime) % hash_mod;
        offset_basis = xor(offset_basis, ord(substr(offset_str,i,1)));
    }
    
    print hash_bits, "bit offset_basis =", offset_basis;
    

    NOTE: The above code fragment example is written in the calc language, not in C.

    FNV-0 Historic note: The FNV-0 is the historic FNV algorithm that is now deprecated. It has an offset_basis of 0. Unless the FNV-0 hash is required for historical purposes, the FNV-1 or FNV-1a should be used in place of the FNV-0 hash. Use FNV-1 and FNV-1a hashes, with their non-zero offset_basis instead. The FNV-0 hashes all buffers that contain only 0 octets to a hash value of 0. The FNV-1 and FNV-1a hash do not suffer from this minor problem.


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A few remarks on FNV primes

While theory behind FNV_prime's is beyond the scope of this web page, the following text may suffice to satisfy the curious:

One of the key properties to look for in an FNV_prime is how it impacts dispersion.

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

256int((5 + 2s)/12) + 28 + b
such that:
  • 0 < b < 28
  • The number of one-bits in b is 4 or 5
  • p mod 240 - 224 - 1 > 224 + 28 + 27

An FNV_prime that matches the above constraints tend to have better dispersion properties. They improve the polynomial feedback characteristic when an FNV_prime multiplies an intermediate hash value. The hash values produced are more scattered throughout the n-bit hash space.

It is a nice side effect that FNV_prime may be optimized by some compilers for some hardware. On some hardware, replacing the FNV_prime multiply with a set of shifts and adds will improve performance. In other cases where multiply may be pipelined (such as in vector mode), the set of shifts and adds may be sub-optimal. The FNV_prime were not selected for compiler optimization, they were selected for the quality of resulting hash function.

In the case where s = 5, both 16777499 and 16777619 could have been used. The narrowness of the 32-bit hash suggested that the larger prime might be better. It turned out that this level of caution was not warranted. When larger FNV hashes were developed, we opted to select the smallest prime. For compatibility with the original IEEE POSIX P1003.2 committee proposal, the historic FNV_prime for the s = 5 case was kept. The requirement that the FNV_prime mod 240 - 224 - 1 (1099494850559) must be > 224 + 28 + 27 (16777600) was added to harmonize the FNV_primes across 4 < s < 11.

The case where s < 5 is not considered because the resulting hash quality is too low. Such small hashes can, if desired, be derived from a 32 bit FNV hash by xor-folding.

The case where s > 10 is considered because 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. The criteria above is a simplified form that fails to generate 2048-bit FNV_prime and a 4096-bit FNV_prime, for example. For such large primes we would need to use a more extensive prime selection criteria.


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Changing the FNV hash size - xor-folding

If you need an x-bit hash where x is not a power of 2, then we recommend that you compute the FNV hash that is just larger than x-bits and xor-fold the result down to x-bits. By xor-folding we mean shift the excess high order bits down and xor them with the lower x-bits.

For example to produce a 24 bit FNV-1 hash in C we xor-fold fold a 32 bit FNV-1 hash:

#define MASK_24 (((u_int32_t)1<<24)-1) /* i.e., (u_int32_t)0xffffff */
#define FNV1_32_INIT ((u_int32_t)2166136261)
u_int32_t hash;
void *data;
size_t data_len;

hash = fnv_32_buf(data, data_len, FNV1_32_INIT);
hash = (hash>>24) ^ (hash & MASK_24);

To produce a 16 bit FNV-1 hash in C we xor-fold fold a 32 bit FNV-1 hash:

#define MASK_16 (((u_int32_t)1<<16)-1) /* i.e., (u_int32_t)0xffff */
#define FNV1_32_INIT ((u_int32_t)2166136261)
u_int32_t hash;
void *data;
size_t data_len;

hash = fnv_32_buf(data, data_len, FNV1_32_INIT);
hash = (hash>>16) ^ (hash & MASK_16);

To produce a 56 bit FNV-1 hash in C (on a machine with 64 bit unsigned values) we xor-fold fold a 64 bit FNV-1 hash:

#define MASK_56 (((u_int64_t)1<<56)-1) /* i.e., (u_int64_t)0xffffffffffffff */
#define FNV1_64_INIT ((u_int64_t)14695981039346656037)
u_int64_t hash;
void *data;
size_t data_len;

hash = fnv_64_buf(data, data_len, FNV1_64_INIT);
hash = (hash>>56) ^ (hash & MASK_56);

The above process assumes that you are using an FNV hash that at most twice as large as the x-bits that you need. For x < 16, there is no 16 bit (or less) FNV-1 hash to use.

For tiny x < 16 bit values, we recommend using a 32 bit FNV-1 hash as follows:

/* NOTE: for 0 < x < 16 ONLY!!! */
#define TINY_MASK(x) (((u_int32_t)1<<(x))-1)
#define FNV1_32_INIT ((u_int32_t)2166136261)
u_int32_t hash;
void *data;
size_t data_len;

hash = fnv_32_buf(data, data_len, FNV1_32_INIT);
hash = (((hash>>x) ^ hash) & TINY_MASK(x));

At the expense of CPU performance, one may use a larger FNV-1 hash that is normally required in any of the above xor-folding examples. This will not produce the same standard output, but it may provide slightly better dispersion at the expense of more CPU time. All that is needed is to use a larger FNV-1 hash and to move the mask outside of the expression on the final statement.

For example, to produce a 24 bit FNV-1 hash could have used a 64 bit FNV-1 hash, in a non-standard way, as follows:

/* NOTE: non-standard use of a larger hash */
#define MASK_24 (((u_int64_t)1<<24)-1) /* i.e., (u_int64_t)0xffffff */
#define FNV1_64_INIT ((u_int64_t)14695981039346656037)
u_int64_t hash;
void *data;
size_t data_len;

hash = fnv_64_buf(data, data_len, FNV1_64_INIT);
hash = (((hash>>24) ^ hash) & MASK_24);

Replacing a 32 bit FNV-1 hash with a 64 bit FNV-1 hash during xor-folding might yield better dispersion at the expense of CPU time. However using an even larger FNV-1 hash is almost certainly a waste of CPU time. If you are going to use this non-standard xor-folding method, we recommend that you only do it for x < 32 bits, and only replace the 32 bit FNV-1 hash with a 64 bit FNV-1 hash.

NOTE: One may substitute the FNV-1a hash for the FNV-1 hash in any of the xor-folding examples. Some people believe that FNV-1a xor-folding gives then slightly better dispersion without any impact on CPU performance. See the FNV-1a hash description for more information.

If you really need an x-bit hash for x > 1024 bits, send us EMail.


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Changing the FNV hash size - non-powers of 2

The FNV hash is designed for hash sizes that are a power of 2. If you need a hash size that is not a power of two, then you have two choices. One method id called the lazy mod mapping method and the other is called the retry method. Both involve mapping a range that is a power of 2 onto an arbitrary range.

  • Lazy mod mapping method: The lazy mod mapping method uses a simple mod on an n-bit hash to yield an arbitrary range. To produce a hash range between 0 and X use a n-bit FNV hash where n is smallest FNV hash that will produce values larger than X without the need for xor-folding.

    For example, to produce a value between 0 and 2142779559 using the lazy mod mapping method, we select a 32-bit FNV hash because:

    232 > 2142779559

    We compute the 32-bit FNV hash value and then perform a final mod:

    #define TRUE_HASH_SIZE ((u_int32_t)2142779560) /* range top plus 1 */
    #define FNV1_32_INIT ((u_int32_t)2166136261)
    u_int32_t hash;
    void *data;
    size_t data_len;
    
    hash = fnv_32_buf(data, data_len, FNV1_32_INIT);
    hash %= TRUE_HASH_SIZE;
    

    An advantage of the lazy mod mapping method is that it requires only 1 more operation: only an additional mod is performed at the end. The disadvantage of the lazy mod mapping method is that there is a bias against the larger values.

    To understand this bias consider the a need to produce a value between 0 and 999999. We will compute a 32-bit FNV hash value because:

    232 > 999999

    We compute the 32-bit FNV hash value using the and then perform the final mod:

    #define TRUE_HASH_SIZE ((u_int32_t)1000000) /* range top plus 1 */
    #define FNV1_32_INIT ((u_int32_t)2166136261)
    u_int32_t hash;
    void *data;
    size_t data_len;
    
    hash = fnv_32_buf(data, data_len, FNV1_32_INIT);
    hash %= TRUE_HASH_SIZE;
    

    The bias introduced by the final mod is slight. The values 0 through 967295 will be created by 4295 different 32-bit FNV hash values whereas the values 967296 through 999999 will be created by only 4294 different 32-bit FNV hash values. In other words, the values 0 through 967295 will occur ~1.0002328 times as often as the values 967296 through 999999.

    The bias can be larger when the range is nearly as large as the range of values produced by the FNV hash. Consider using the lazy mod mapping method to produce values between 0 and 9999999999999999999. We use a 64-bit FNV hash because:

    264 > 9999999999999999999

    We compute the 64-bit FNV hash value using the and then perform the final mod:

    #define TRUE_HASH_SIZE ((u_int64_t)10000000000000000000) /* range top plus 1 */
    #define FNV1_64_INIT ((u_int64_t)14695981039346656037)
    u_int64_t hash;
    void *data;
    size_t data_len;
    
    hash = fnv_64_buf(data, data_len, FNV1_64_INIT);
    hash %= TRUE_HASH_SIZE;
    

    Here the bias introduced by the final mod is more noticeable. The values 0 through 9999999999999999999 will be created by 2 different 64-bit FNV hash values whereas the values 10000000000000000000 through 18446744073709551615 will be created by only 1 64-bit FNV hash value.

    NOTE: This bias issue may not be of concern to you, but we thought we should point out this issue just in case you care. Many applications should / will not care about this bias. Most applications can use the lazy mod mapping method without any problems. Your application, may vary however.

    NOTE: One may substitute the FNV-1a hash for the FNV-1 hash in any of the lazy mod mapping method examples. Some people believe that FNV-1a lazy mod mapping method gives then slightly better dispersion without any impact on CPU performance. See the FNV-1a hash description for more information.

  • Retry method: The retry method also performs a final mod in order to produce a hash range between 0 and X. Unlike lazy mod mapping method, the retry method avoids the bias by additional computation.

    To produce a hash range between 0 and X use a n-bit FNV hash where n is smallest FNV hash that will produce values larger than X without the need for xor-folding.

    For example, to produce a value between 0 and 49999 using the retry method, we select a 32-bit FNV hash because:

    232 > 49999

    Before the final mod 50000 is performed, we check to see if the 32-bit FNV hash value is one of the upper biased values. If it is, we perform additional loop cycles until is below the bias level. For example:

    #define TRUE_HASH_SIZE ((u_int32_t)50000) /* range top plus 1 */
    #define FNV_32_PRIME ((u_int32_t)16777619)
    #define FNV1_32_INIT ((u_int32_t)2166136261)
    #define MAX_32BIT ((u_int32_t)0xffffffff) /* largest 32 bit unsigned value */
    #define RETRY_LEVEL ((MAX_32BIT / TRUE_HASH_SIZE) * TRUE_HASH_SIZE)
    u_int32_t hash;
    void *data;
    size_t data_len;
    
    hash = fnv_32_buf(data, data_len, FNV1_32_INIT);
    while (hash >= RETRY_LEVEL) {
        hash = (hash * FNV_32_PRIME) + FNV1_32_INIT;
    }
    hash %= TRUE_HASH_SIZE;
    

    The disadvantage of the retry method is that it sometimes requires additional calculations. An advantage of the retry method it avoids slightly biased values.

    For another example, we will produce a value between 0 and 999999999999 using the retry method, we select a 64-bit FNV hash because:

    264 > 999999999999

    Before the final mod 1000000000000 is performed, we check to see if the 64-bit FNV hash value is one of the upper biased value. If it is, we perform additional loop cycles until it is not.

    #define TRUE_HASH_SIZE ((u_int64_t)1000000000000) /* range top plus 1 */
    #define FNV_64_PRIME ((u_int64_t)1099511628211)
    #define FNV1_64_INIT ((u_int64_t)14695981039346656037)
    #define MAX_64BIT ((u_int64_t)0xffffffffffffffff) /* largest 64 bit unsigned value */
    #define RETRY_LEVEL ((MAX_64BIT / TRUE_HASH_SIZE) * TRUE_HASH_SIZE)
    u_int64_t hash;
    void *data;
    size_t data_len;
    
    hash = fnv_64_buf(data, data_len, FNV1_64_INIT);
    while (hash >= RETRY_LEVEL) {
        hash = (hash * FNV_64_PRIME) + FNV1_64_INIT;
    }
    hash %= TRUE_HASH_SIZE;
    

    NOTE: One may substitute the FNV-1a hash for the FNV-1 hash in any of the retry method examples. Some people believe that FNV-1a retry method gives then slightly better dispersion without any impact on CPU performance. See the FNV-1a hash description for more information.

  • To summarize: When dealing with an application that needs to generate a hash value over an arbitrary range, one can do one of the following:

    1. Change the application to use hash values that range between 0 and 2n-1. Use a n-bit FNV hash or xor-folding if needed.

      Pro: Yields the best results in the shortest amount of CPU time.
      Con: Requires source code change to force hash range to be a power of 2 in size.

    2. Use the lazy mod mapping method if one does not care about the slight hash bias and does not want (or cannot change) the hash range.

      Pro: Yields the fastest results for a non-power of 2 range.
      Con: Produces a slight bias against larger hash values. However if one does not care about the slight bias, then there is no problem using this technique.

    3. Use the retry method if one wants to avoid the hash bias and does not want / cannot change the hash range.

      Pro: Produces non-biased values for a non-power of 2 range.
      Con: Requires slightly more CPU time in some cases.


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FNV source

FNV reference source

In the C source< below, primes are provided for 32 bit and 64 bit unsigned integers. For compilers that do not implement the unsigned long long type, code is provided to quickly simulate the 64 bit multiply by the particular FNV_prime.

  • fnv-5.0.3.tar.gz - (all the bits) [updated: 2012 May 20]

  • hash_32.c - (32 bit FNV-1 algorithm)
  • hash_64.c - (64 bit FNV-1 algorithm)
  • hash_32a.c - (32 bit FNV-1a algorithm)
  • hash_64a.c - (64 bit FNV-1a algorithm)
  • fnv.h - (FNV header file)

  • fnv32.c - (32 bit FNV-0, FNV-1, and FNV-1a hash tool/demo) [updated: 2012 May 20]
  • fnv64.c - (64 bit FNV-0, FNV-1, and FNV-1a hash tool/demo) updated: 2012 May 20]

  • README - (brief comments about FNV-0, FNV-1, and FNV-1a)
  • Makefile - (how to compile/install)
  • have_ulong64.c - (64 bit unsigned integer type detector)
  • test_fnv.c - (FNV test vectors)
NOTE: As of version 5.0, the above source include test vectors for 32 bit and 64 bit versions of the FNV-0, FNV-1, and FNV-1a algoritms. The test_fnv.c file contains validated test vectors. To verify a compiled code, try:
make check
For compiled code, try:
  • fnv032 -t 1 -v
  • fnv132 -t 1 -v
  • fnv1a32 -t 1 -v
  • fnv064 -t 1 -v
  • fnv164 -t 1 -v
  • fnv1a64 -t 1 -v
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Other FNV source code

Andy Allinger sent us this 32 bit FNV-1a subroutine written in FNV-1 in FORTRAN.

Nicola Bonelli has an implementation of FNV using the iovec interface:

Nicola Bonelli also wrote the following C++ FNV implementation:

Georgi Marinov (Georgi 'Kaze' 'Sanmayce') posted his very fast FNV-1a implementation:

Wayne Diamond implemented 32-bit FNV algorithm in PowerBASIC inline x86 assembly:


FUNCTION FNV32(BYVAL dwOffset AS DWORD, BYVAL dwLen AS DWORD, BYVAL offset_basis AS DWORD) AS DWORD
#REGISTER NONE
! mov esi, dwOffset ;esi = ptr to buffer
! mov ecx, dwLen ;ecx = length of buffer (counter)
! mov eax, offset_basis ;set to 2166136261 for FNV-1
! mov edi, &h01000193 ;FNV_32_PRIME = 16777619
! xor ebx, ebx ;ebx = 0
nextbyte:
! mul edi ;eax = eax * FNV_32_PRIME
! mov bl, [esi] ;bl = byte from esi
! xor eax, ebx ;al = al xor bl
! inc esi ;esi = esi + 1 (buffer pos)
! dec ecx ;ecx = ecx - 1 (counter)
! jnz nextbyte ;if ecx is 0, jmp to NextByte
! mov FUNCTION, eax ;else, function = eax
END FUNCTION

Wayne said:

''Just thought I should let you know that I've ported the 32-bit FNV algorithm over to inline assembly. It's actually in PowerBASIC (www.powerbasic.com) format - a compiler I use, but the main function is all assembly. It could be optimized further in terms of saving a couple of clock cycles, but it's fairly optimized al ready - only 6 instructions in the main loop, plus 5 setup instructions, and compiles to just 33 bytes.''

M.S.Schulte sent us these 32-bit FNV-1 and FNV-1a x86 assembler implementations (written in flat assembler), half of which were optimized for speed, the other half were optimized for size:


small_fnv32: ;FNV1 32bit (size: 31 bytes)
; Intel Core 2 Duo E6600: 354.20 mb/s
   push esi
   push edi
   mov esi, [esp + 0ch] ;buffer
   mov ecx, [esp + 10h] ;length
   mov eax, [esp + 14h] ;basis
   mov edi, 01000193h ;fnv_32_prime
 next:
   mul edi
   xor al, [esi]
   inc esi
   loop snext
   pop edi
   pop esi
   retn 0ch

 small_fnv32a: ;FNV1a 32bit (size: 31 bytes)
; Intel Core 2 Duo E6600: 327.68 mb/s
   push esi
   push edi
   mov esi, [esp + 0ch] ;buffer
   mov ecx, [esp + 10h] ;length
   mov eax, [esp + 14h] ;basis
   mov edi, 01000193h ;fnv_32_prime
 nexta:
   xor al, [esi]
   mul edi
   inc esi
   loop nexta
   pop edi
   pop esi
   retn 0ch

fast_fnv32: ;FNV1 32bit (size: 36 bytes)
; Intel Core 2 Duo E6600: 565.12 mb/s
   push ebx
   push esi
   push edi
   mov esi, [esp + 10h] ;buffer
   mov ecx, [esp + 14h] ;length
   mov eax, [esp + 18h] ;basis
   mov edi, 01000193h ;fnv_32_prime
   xor ebx, ebx
 next:
   mul edi
   mov bl, [esi]
   xor eax, ebx
   inc esi
   dec ecx
   jnz next
   pop edi
   pop esi
   pop ebx
   retn 0ch

 fast_fnv32a: ;FNV1a 32bit (size: 36 bytes)
; Intel Core 2 Duo E6600: 574.95 mb/s
   push ebx
   push esi
   push edi
   mov esi, [esp + 10h] ;buffer
   mov ecx, [esp + 14h] ;length
   mov eax, [esp + 18h] ;basis
   mov edi, 01000193h ;fnv_32_prime
   xor ebx, ebx
 nexta:
   mov bl, [esi]
   xor eax, ebx
   mul edi
   inc esi
   dec ecx
   jnz nexta
   pop edi
   pop esi
   pop ebx
   retn 0ch

M.S.Schulte also sent us these 64-bit FNV-1 and FNV-1a x86 assembler implementations:


;FNV64 x86-64bit assembler implementation (written in flat assembler)
;FNV64-1 and FNV64-1a, both 37 bytes, (~284.13 mb/s Intel E8400)
;invoke fnv64,buffer,length,base (x64 Calling Convention)

  fnv64:
    mov rax, r8
    mov r8, rdx
    mov r9, 100000001b3h ;fnv_64_prime
    xor r10, r10
  next:
    mul r9
    mov r10b, [rcx]
    xor rax, r10
    inc rcx
    dec r8
    jnz next
    ret

  fnv64a:
    mov rax, r8
    mov r8, rdx
    mov r9, 100000001b3h ;fnv_64_prime
    xor r10, r10
  nexta:
    mov r10b, [rcx]
    xor rax, r10
    mul r9
    inc rcx
    dec r8
    jnz nexta
    ret


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gcc optimization

It has been reported by several people that under the gcc compiler with -O3 on many AMD & Intel CPUs, that replacing the FNV_prime multiply with a expression of shifts and adds will improve the performance.

Limited testing on our part confirmed that one can gain a few % in speed on an 1.6GHz AMD Athlon using gcc version 3.2.2 with -O3 optimization.

For a 32 bit FNV-1, we used:

while (bp < be) {

    /* multiply by the 32 bit FNV magic prime mod 2^32 */
#if defined(NO_FNV_GCC_OPTIMIZATION)
    hval *= FNV_32_PRIME;
#else
    hval += (hval<<1) + (hval<<4) + (hval<<7) + (hval<<8) + (hval<<24);
#endif

    /* xor the bottom with the current octet */
    hval ^= (uint32_t)(*bp++);
}

For a 32 bit FNV-1a, we used:

while (bp < be) {

    /* xor the bottom with the current octet */
    hval ^= (uint32_t)(*bp++);

    /* multiply by the 32 bit FNV magic prime mod 2^32 */
#if defined(NO_FNV_GCC_OPTIMIZATION)
    hval *= FNV_32_PRIME;
#else
    hval += (hval<<1) + (hval<<4) + (hval<<7) + (hval<<8) + (hval<<24);
#endif
}

For a 64 bit FNV-1, we used:

while (bp < be) {

    /* multiply by the 64 bit FNV magic prime mod 2^64 */
#if defined(NO_FNV_GCC_OPTIMIZATION)
    hval *= FNV_64_PRIME;
#else
    hval += (hval << 1) + (hval << 4) + (hval << 5) +
            (hval << 7) + (hval << 8) + (hval << 40);
#endif

    /* xor the bottom with the current octet */
    hval ^= (uint64_t)(*bp++);
}

For a 64 bit FNV-1a, we used:

while (bp < be) {

    /* xor the bottom with the current octet */
    hval ^= (uint64_t)(*bp++);

    /* multiply by the 64 bit FNV magic prime mod 2^64 */
#if defined(NO_FNV_GCC_OPTIMIZATION)
    hval *= FNV_64_PRIME;
#else
    hval += (hval << 1) + (hval << 4) + (hval << 5) +
            (hval << 7) + (hval << 8) + (hval << 40);
#endif
}


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Can you help solve some of the zero-hash challenges?

We are interested in finding the shortest data sets, under certain constraints, that produce a FNV hash value of zero for the various sizes of the FNV-1 and FNV-1a hash function. Those who offer the best solution will receive fame and credit on the FNV web page.

If you have a zero-value hash solution to an unsolved challenge, or if you have a better (shorted data segment) solution than one that is shown below, please send EMail to:

fnv EMail addr

Please use the subject line:

zero-hash challenge solution

NOTE: Please use the solution format used by Russ Cox (see below), if possible.

Please include the following information in your EMail message:

  1. The challenge number you claim to have solved
  2. The name of the challenge you claim to have solved
  3. The length, in octets (8 bit bytes) of your proposed solution
  4. Who should we credit (i.e., how do you want us to credit you on our web page) for solving the challenge?
  5. A URL containing your proposed solution (optional)
NOTE: If your solution is large, please do not send the data set in the EMail. Instead send is a URL where we can download your proposed challenge solution.
Zero-hash challenges:
  1. SOLVED! What is the shortest binary data set for which the 32-bit FNV-1 hash is 0?
    32-bit solution by Russ Cox <rcs Email address> on 2011-Mar-02:
    There are 254 solutions of length 5, ranging from
    
    FNV32_1(01 47 6c 10 f3) = 0
    
    to
    
    FNV32_1(fd 45 41 08 a0) = 0
    

  2. SOLVED! What is the shortest binary data set for which the 64-bit FNV-1 hash is 0?
    Scott Pakin <pakin Email address> on 2011-Aug-22 reported that there are no solutions for binary data sets of length 7 or less.

    64-bit solution by an anonymous scientist <ntldr Email address> on 2011-Oct-23:

    There are no solutions for length 8.
    
    These are the solutions for length 9:
    
    FNV64_1(92 06 77 4c e0 2f 89 2a d2) = 0
    FNV64_1(fb 6c 4f db 00 41 db c0 fe) = 0
    FNV64_1(9f 72 72 35 80 4b 8d 6b 06) = 0
    FNV64_1(3d 82 76 00 80 7c 52 62 1a) = 0
    FNV64_1(58 21 f5 a2 e1 01 9d 80 e0) = 0
    FNV64_1(52 a1 eb 10 a0 e9 45 96 05) = 0
    FNV64_1(be 64 8a 14 e1 46 17 18 ff) = 0
    FNV64_1(9e 50 1d f2 41 75 55 ac 05) = 0
    FNV64_1(b3 92 a9 6f 80 e4 29 a4 63) = 0
    FNV64_1(82 ba b3 41 81 0f db 83 15) = 0
    FNV64_1(92 f4 6e 0e e1 b9 e5 45 2d) = 0
    FNV64_1(3c ea 57 50 81 67 67 9b e0) = 0
    FNV64_1(36 e3 96 34 e2 1d 36 00 61) = 0
    FNV64_1(af fa ff ee 61 b0 5e c4 04) = 0
    FNV64_1(d5 c9 88 15 02 2f d3 38 c2) = 0
    FNV64_1(bc a7 38 51 e2 2f b1 1b 22) = 0
    FNV64_1(70 f2 10 ba 02 45 37 b3 e8) = 0
    FNV64_1(5b a3 a0 4e 81 fc 4f 32 5b) = 0
    FNV64_1(cd 50 99 68 22 d4 78 2f b0) = 0
    FNV64_1(fa ff 0d fa e2 f0 43 b4 9a) = 0
    FNV64_1(16 3f ba 47 43 94 44 fe 86) = 0
    FNV64_1(46 e0 03 71 c2 57 f0 bc da) = 0
    FNV64_1(60 74 4a 52 e3 06 42 36 f2) = 0
    FNV64_1(97 20 3a f8 a2 f6 8a 62 a6) = 0
    FNV64_1(98 f5 cc d5 03 32 22 1a e2) = 0
    FNV64_1(5d d5 14 e8 e3 43 8b 5a 9e) = 0
    FNV64_1(95 b8 11 62 03 5a ed d2 cb) = 0
    FNV64_1(f9 cb 23 1d 03 71 c5 ca 5c) = 0
    FNV64_1(c3 04 1c 59 82 a5 aa 9b 55) = 0
    FNV64_1(68 10 80 61 a3 5e 72 31 48) = 0
    FNV64_1(43 0a eb 89 c2 c1 9d d8 2a) = 0
    FNV64_1(5a a3 e3 40 23 ce 90 bc a2) = 0
    FNV64_1(27 e1 3f aa a3 8f af 6a 51) = 0
    FNV64_1(0c 5b ac 36 24 22 a2 7c 24) = 0
    FNV64_1(ea bc d7 7c 24 49 58 66 57) = 0
    FNV64_1(5a 30 62 51 83 9c 97 c3 75) = 0
    FNV64_1(7a 18 75 d3 c3 88 65 0b 3a) = 0
    FNV64_1(02 38 25 95 25 0b 3b 0c a8) = 0
    FNV64_1(33 1c ae dd 83 fc 55 f4 63) = 0
    FNV64_1(cb 87 3d b9 e5 38 0b bd ca) = 0
    FNV64_1(3a 25 ba 67 a4 c7 49 80 e9) = 0
    FNV64_1(49 14 3b 94 05 63 b5 de d6) = 0
    FNV64_1(45 fb 0d 28 45 19 66 63 27) = 0
    FNV64_1(92 7a e5 a6 e5 88 ba 55 68) = 0
    FNV64_1(c3 93 7c 11 c4 1a 2f e0 8b) = 0
    FNV64_1(a1 d8 5e 71 a5 6a 96 5e 64) = 0
    FNV64_1(77 7b d7 7d 05 dc 73 64 c3) = 0
    FNV64_1(3d 3f d4 d6 a6 71 b2 9d 65) = 0
    FNV64_1(8d 45 9e d0 27 66 b4 46 34) = 0
    FNV64_1(f1 da 16 a1 85 fe 43 a7 30) = 0
    FNV64_1(97 6b 02 e3 66 10 3d 6e ab) = 0
    FNV64_1(84 2b d9 13 a7 25 5a 8a 22) = 0
    FNV64_1(0c 2b 2f d2 28 3a 91 df 95) = 0
    FNV64_1(1c 01 ed aa 47 2f 64 6a 8b) = 0
    FNV64_1(71 66 6f 98 47 74 48 eb 39) = 0
    FNV64_1(2b b3 61 de e8 6c 33 fd 32) = 0
    FNV64_1(c5 33 7e c3 87 9c 0c 24 4b) = 0
    FNV64_1(b7 44 ea 2c a8 59 bc fc c5) = 0
    FNV64_1(b2 8c 40 98 67 46 6f ce 35) = 0
    FNV64_1(04 34 61 b3 87 d4 e5 1a 7f) = 0
    FNV64_1(20 ba 15 17 e8 dd d9 f6 19) = 0
    FNV64_1(36 c4 d3 ef 88 53 6e 86 56) = 0
    FNV64_1(32 55 ce f0 48 73 af 8d 9d) = 0
    FNV64_1(18 3c d8 70 08 71 6a 47 a3) = 0
    FNV64_1(a8 ad fb 29 a8 e4 8e 82 c4) = 0
    FNV64_1(47 47 bf 58 08 7f ab bc 34) = 0
    FNV64_1(8f 68 71 3a e9 56 8f d0 0f) = 0
    FNV64_1(64 5e dc 14 88 93 8d b4 35) = 0
    FNV64_1(b4 33 d0 6d 48 bb 3a 5d 3d) = 0
    FNV64_1(22 e4 4d 0a 48 bd 95 1e 8e) = 0
    FNV64_1(78 6e 06 7d 48 ce db 12 33) = 0
    FNV64_1(7e 1f 4d 02 48 f8 d2 a5 c2) = 0
    FNV64_1(90 6b 26 4e c7 ef 12 f2 20) = 0
    FNV64_1(90 10 a8 21 09 16 22 57 bc) = 0
    FNV64_1(5b 1a 8c bc 09 2c a4 2d 9c) = 0
    FNV64_1(2c 1a 6e 44 a9 7d 98 e0 39) = 0
    FNV64_1(8a 2b 35 ab 49 97 d5 f7 bc) = 0
    FNV64_1(29 bc 62 5e 0a 4e 9e 34 40) = 0
    FNV64_1(e7 e6 c7 00 aa d3 26 5a 4a) = 0
    FNV64_1(7e 65 e5 51 2b 66 e8 b5 b2) = 0
    FNV64_1(2b d7 cf 6a 6a 6f b4 56 c9) = 0
    FNV64_1(33 51 09 af ab 42 80 8b 07) = 0
    FNV64_1(d1 78 30 6b c9 9c af 1f d4) = 0
    FNV64_1(c6 00 f9 bf 4b 38 f0 00 c6) = 0
    FNV64_1(a1 81 99 9a c9 f2 8e 4c 6f) = 0
    FNV64_1(b3 d1 6c 57 2c 62 3c b0 5c) = 0
    FNV64_1(c7 50 c1 4d ec de 91 e8 fd) = 0
    FNV64_1(54 51 fe aa ec e9 6b f2 a2) = 0
    FNV64_1(5d dc 27 f3 4b c8 b0 9a c9) = 0
    FNV64_1(d2 4d e1 77 8c 0a 8f 2d 44) = 0
    FNV64_1(ce e4 e5 80 ca 8a 07 dc 67) = 0
    FNV64_1(0f d0 8f 67 ca 9f 94 a5 86) = 0
    FNV64_1(89 e9 ed dd ed 84 84 50 26) = 0
    FNV64_1(76 f5 be 03 ac 82 5a 09 26) = 0
    FNV64_1(f8 71 02 ca 6c 6d a5 ae fc) = 0
    FNV64_1(e8 cb 80 56 ad 00 a0 d1 d2) = 0
    FNV64_1(88 89 0c dd 0c cf b2 5d d7) = 0
    FNV64_1(69 ad 8f db 0d 03 8a ca 37) = 0
    FNV64_1(96 58 24 93 cb bf d7 f1 fe) = 0
    FNV64_1(ee b1 f6 d2 6d 9b 46 7d 3f) = 0
    FNV64_1(de 64 18 d6 2e 86 5b 3c 0c) = 0
    FNV64_1(24 05 66 e4 0d f1 c8 b1 d3) = 0
    FNV64_1(77 d7 5f 5f ef 81 2d b3 37) = 0
    FNV64_1(58 53 f5 b5 2e ec 51 fe 25) = 0
    FNV64_1(ba 65 2a 3b 8e c6 bb a8 b6) = 0
    FNV64_1(e5 81 4f 09 f0 0c ec f9 fa) = 0
    FNV64_1(50 5b e8 f9 f0 6a 47 b4 64) = 0
    FNV64_1(d3 0e f4 c7 6e d9 60 31 b5) = 0
    FNV64_1(58 e4 4a 3c cd 97 d6 fd 84) = 0
    FNV64_1(6f 82 aa ca 2f e7 1a 8d b1) = 0
    FNV64_1(8f 50 ec 2f 2f e7 30 4c db) = 0
    FNV64_1(f0 3b 01 db 6f 33 db 82 41) = 0
    FNV64_1(13 3c 71 e4 8f 75 46 48 8f) = 0
    FNV64_1(2f a5 a5 41 cd f5 b4 c6 45) = 0
    FNV64_1(8b 1a 4c 12 30 38 c3 61 08) = 0
    FNV64_1(6f 9c 5c 3f 8f d6 47 70 f7) = 0
    FNV64_1(c1 0e 16 18 50 1b 47 48 f8) = 0
    FNV64_1(2b 94 3f ad 30 ad 5e c4 85) = 0
    FNV64_1(5f 55 92 c6 ce b9 f5 05 08) = 0
    FNV64_1(42 8e 3a bb f1 bd 08 09 25) = 0
    FNV64_1(28 84 f5 2b ce f1 3e 47 41) = 0
    FNV64_1(25 d1 2c bf 90 5c 71 24 85) = 0
    FNV64_1(d0 25 3d f3 90 64 67 ae f9) = 0
    FNV64_1(c5 1d e5 36 11 a9 7b 4d e0) = 0
    FNV64_1(88 c2 24 da 50 f9 55 03 dc) = 0
    FNV64_1(ff 54 4f 75 cf 6d bb c4 4b) = 0
    FNV64_1(9e 49 c2 63 11 d7 b0 74 25) = 0
    FNV64_1(ac b1 42 65 cf 7d 84 0e 37) = 0
    FNV64_1(05 a5 28 18 11 e3 0d 6a aa) = 0
    FNV64_1(03 8d 11 ce f2 6f 0e 0a cf) = 0
    FNV64_1(bf d6 88 3d 51 75 18 67 0e) = 0
    FNV64_1(69 a2 dd 69 cf e4 94 5e e3) = 0
    FNV64_1(e4 62 0b 95 b1 58 a1 d4 25) = 0
    FNV64_1(c0 75 c6 ec 51 9e d4 c7 4c) = 0
    FNV64_1(83 9d b3 97 32 54 9b 04 ec) = 0
    FNV64_1(9a 7f 71 94 32 cf bb 97 38) = 0
    FNV64_1(7a 4f e4 60 13 93 fd 7d 50) = 0
    FNV64_1(76 48 71 f5 52 2f cb f7 e2) = 0
    FNV64_1(da 0e 88 1f 13 ba d5 a7 2f) = 0
    FNV64_1(2a be ca e7 33 12 4e 33 26) = 0
    FNV64_1(79 ce 5e ee 92 27 5d c7 17) = 0
    FNV64_1(36 91 77 d3 72 5a de 9f 0b) = 0
    FNV64_1(3a 33 cd 8d 52 7a b8 2a d8) = 0
    FNV64_1(25 66 ec c3 52 8b d0 13 4f) = 0
    FNV64_1(de d7 a1 1f b2 58 65 d8 d7) = 0
    FNV64_1(8a e5 cb 54 33 b0 de 92 42) = 0
    FNV64_1(71 49 0a bb 33 d8 35 b3 59) = 0
    FNV64_1(03 36 3b 64 f4 98 4b 21 99) = 0
    FNV64_1(8c f5 50 02 d2 10 db 86 1d) = 0
    FNV64_1(c3 4f cf 6e 93 4e b5 d8 b4) = 0
    FNV64_1(2a fb 95 75 73 8c 85 76 82) = 0
    FNV64_1(35 c0 2a 8b f5 56 45 66 45) = 0
    FNV64_1(68 2a 76 44 73 cf 31 3a 8e) = 0
    FNV64_1(98 4c a0 05 93 9a cf 65 a1) = 0
    FNV64_1(a5 3e 3b f8 94 0e 6e 74 73) = 0
    FNV64_1(4b 75 16 e9 35 47 e2 af 21) = 0
    FNV64_1(3c 84 fb ee f6 10 6c 09 3f) = 0
    FNV64_1(45 52 87 53 74 7c 1b 2c a1) = 0
    FNV64_1(a0 8b 28 e0 d3 34 be 90 cb) = 0
    FNV64_1(67 57 50 d0 16 3c 23 af e1) = 0
    FNV64_1(a8 a6 4d 44 16 52 57 ba 95) = 0
    FNV64_1(9e 0c be 6a 75 1d 3f 6c 20) = 0
    FNV64_1(14 1b 43 7a b5 4e 40 88 b0) = 0
    FNV64_1(68 3b bd d6 f7 ae d7 f9 28) = 0
    FNV64_1(ab c0 61 a3 76 20 b8 f7 3b) = 0
    FNV64_1(05 e8 00 91 b5 dd be 7e af) = 0
    FNV64_1(14 dd 60 a4 96 19 04 05 16) = 0
    FNV64_1(7e e5 14 cd 76 87 03 4c 2d) = 0
    FNV64_1(07 f0 09 29 18 7d 7d fe 8a) = 0
    FNV64_1(b9 b4 a5 c6 37 99 fd 49 ff) = 0
    FNV64_1(d2 dd 5a 63 37 e4 08 8e d4) = 0
    FNV64_1(a2 0b f2 5e 76 fd 65 2c 80) = 0
    FNV64_1(c8 d7 df ba 37 e8 d9 2b 0c) = 0
    FNV64_1(6e 40 03 eb 37 ea eb a6 93) = 0
    FNV64_1(27 f9 53 0f 37 fc 0e 28 60) = 0
    FNV64_1(c2 72 49 23 d5 ce 7e bb ef) = 0
    FNV64_1(3e 11 d8 6b b6 e9 30 2f ab) = 0
    FNV64_1(0e dd b7 d7 19 45 86 d7 79) = 0
    FNV64_1(a3 f7 21 85 97 07 7d e1 4b) = 0
    FNV64_1(4e 76 21 ee 19 67 54 55 23) = 0
    FNV64_1(0f 19 18 da 38 60 1c 0b 9c) = 0
    FNV64_1(a4 91 5d 2c 77 7f b4 cb c6) = 0
    FNV64_1(c1 b7 ee 41 19 7a 60 4d 7e) = 0
    FNV64_1(88 47 7b 0c d6 4c e0 c1 20) = 0
    FNV64_1(73 88 eb 4f d6 53 4f 7c 6a) = 0
    FNV64_1(f4 5a e5 b3 f9 cf 96 88 8f) = 0
    FNV64_1(ba 5c b1 28 58 2f 33 16 cc) = 0
    FNV64_1(04 cd 1f c8 1a 7a 20 f1 d0) = 0
    FNV64_1(5f 2c 1c 63 b8 48 83 82 a4) = 0
    FNV64_1(22 f5 ed a6 98 51 eb a3 f8) = 0
    FNV64_1(f8 6b 6d 33 fa 65 24 bd 5c) = 0
    FNV64_1(10 3b b6 ae d7 86 73 25 d3) = 0
    FNV64_1(52 31 6c 5a 79 03 be 55 95) = 0
    FNV64_1(af c9 ab 5e 1b 54 de 1d 84) = 0
    FNV64_1(c2 ed f4 36 79 77 81 0d ee) = 0
    FNV64_1(36 f5 db eb d8 30 d9 69 f6) = 0
    FNV64_1(43 84 92 b9 79 90 66 a4 e6) = 0
    FNV64_1(7d e9 4d 0e 1b da 69 eb 57) = 0
    FNV64_1(2d 03 20 62 fb 3b 6e 88 65) = 0
    FNV64_1(e5 69 ec d2 79 be d8 aa 8e) = 0
    FNV64_1(ac 26 0a dd fb 68 43 1f 6d) = 0
    FNV64_1(3c 96 c1 be 3a be 22 ae 76) = 0
    FNV64_1(de 73 09 f1 1c 39 67 8a 0c) = 0
    FNV64_1(56 2e 5f 2c 3a fd 30 40 7d) = 0
    FNV64_1(68 57 ce 1c 59 e0 e0 eb 04) = 0
    FNV64_1(df f7 e6 75 1c 66 88 86 90) = 0
    FNV64_1(fd af f5 8b 5a 06 ae 0b 40) = 0
    FNV64_1(4e cf a7 e9 1c 93 af 36 a8) = 0
    FNV64_1(56 dc 13 cf fc 12 88 bb b8) = 0
    FNV64_1(1f 5f c2 b2 3b 75 fb 7c 92) = 0
    FNV64_1(4e 9c bb ba 5a 74 e3 a4 e1) = 0
    FNV64_1(0b a0 c8 c5 1d 99 06 87 5e) = 0
    FNV64_1(ff ef b0 25 1d f4 9d df db) = 0
    FNV64_1(09 67 cb 8f 7c 13 3c 75 97) = 0
    FNV64_1(05 bf fe 4d fd d2 6e 61 64) = 0
    FNV64_1(a4 d7 4b 6d 3d 2a bb ee 4c) = 0
    FNV64_1(b9 8c 01 cb 5b f2 50 15 f0) = 0
    FNV64_1(31 45 17 91 1e a3 7f 25 52) = 0
    FNV64_1(10 6c 0c 98 db 0f 9b 1e 88) = 0
    FNV64_1(06 ec cc b6 9b da a2 3a 16) = 0
    FNV64_1(23 66 38 19 7c ac 80 d3 78) = 0
    FNV64_1(b8 f3 d7 98 bc 11 60 0f bf) = 0
    FNV64_1(27 24 2d a8 db c2 99 28 65) = 0
    FNV64_1(64 61 39 c2 bc 79 b5 b1 a6) = 0
    FNV64_1(df ff 2a 12 5c fb 42 6d 01) = 0
    FNV64_1(af 1d ea 4e ff 0d 46 95 5e) = 0
    FNV64_1(2a b0 c6 54 9c e9 98 43 e1) = 0
    FNV64_1(7c e5 9e 74 7d c8 44 ef 9e) = 0
    FNV64_1(56 14 d1 31 dc ce 77 17 c3) = 0
    FNV64_1(ed 6b 65 68 3f 05 36 41 9b) = 0
    FNV64_1(2f d2 24 7e dd 19 4f 91 72) = 0
    FNV64_1(c8 96 f0 54 9d 92 5b cc b1) = 0
    FNV64_1(47 5d 76 63 be 17 24 ad d4) = 0
    FNV64_1(4f 88 0b 03 9e 4a 48 ee 14) = 0
    FNV64_1(26 ec 1b 56 5e b8 5d 5e 39) = 0
    FNV64_1(c3 a8 2d 1a 5e fc b7 81 49) = 0
    FNV64_1(14 3a 3b 0b be e7 b2 4d 75) = 0
    FNV64_1(27 a0 f4 22 df b5 b6 5e 4a) = 0
    

  3. Partial solution: What is the shortest binary data set for which the 128-bit FNV-1 hash is 0?

    Richard Heylen <richard_in_reading Email address> found a 128-bit FNV-1 solution on 2011-Dec-01:
    The following is a solution of length 17:
    
    FNV128_1(20 28 4e 43 40 55 6f 99 25 1b 89 f4 a8 18 ec 76 c0) = 0
    
    NOTE: It is not known if the above solution is the shortest 128-bit FNV-1 solution.

    Can you find a shorter solution or prove that the shortest solutions are of length 17?

  4. Partial solution: What is the shortest binary data set for which the 256-bit FNV-1 hash is 0?

    Richard Heylen <richard_in_reading Email address> found a 256-bit FNV-1 solution on 2011-Dec-17:
    The following is a solution of length 37:
    
    FNV256_1(04 03 F4 7D 37 15 6D DB 3B 06 68 6F 07 0E 0E 3B 67 6E 43 53 0B
    5F 5A 08 93 09 16 29 47 D9 4C 1B BD 7E 04 17 38) = 0
    NOTE: It is not known if the above solution is the shortest 256-bit FNV-1 solution.

    Richard Heylen speculates that the shortest solution might be 32 or 33 in length.

    Can you find a shorter solution or prove that the shortest solutions are of length 37?

  5. What is the shortest binary data set for which the 512-bit FNV-1 hash is 0?

  6. What is the shortest binary data set for which the 1024-bit FNV-1 hash is 0?

  7. SOLVED! What is the shortest binary data set for which the 32-bit FNV-1a hash is 0?
    32-bit solution by Russ Cox <rcs Email address> on 2011-Mar-02:
    The solutions of length 4 are:
    
    FNV32_1a(cc 24 31 c4) = 0
    FNV32_1a(e0 4d 9f cb) = 0
    

  8. SOLVED! What is the shortest binary data set for which the 64-bit FNV-1a hash is 0?
    Scott Pakin <pakin Email address> on 2011-Aug-22 reported that there are no solutions for binary data sets of length 7 or smaller.

    64-bit solution by an anonymous scientist <ntldr Email address> on 2011-Oct-23:

    The only solution for length 8 is:
    
    FNV64_1a(d5 6b b9 53 42 87 08 36) = 0
    

  9. What is the shortest binary data set for which the 128-bit FNV-1a hash is 0?

  10. What is the shortest binary data set for which the 256-bit FNV-1a hash is 0?

  11. What is the shortest binary data set for which the 512-bit FNV-1a hash is 0?

  12. What is the shortest binary data set for which the 1024-bit FNV-1a hash is 0?

    NOTE: By binary data set we mean any arbitrary collection of bits that is a multple of 8 bits (1 octet) in length.

  13. SOLVED! What is the shortest set of consecutive NUL octets for which the 32-bit FNV-1 hash is 0?

  14. SOLVED! What is the shortest set of consecutive NUL octets for which the 64-bit FNV-1 hash is 0?

  15. SOLVED! What is the shortest set of consecutive NUL octets for which the 128-bit FNV-1 hash is 0?

  16. SOLVED! What is the shortest set of consecutive NUL octets for which the 256-bit FNV-1 hash is 0?

  17. SOLVED! What is the shortest set of consecutive NUL octets for which the 512-bit FNV-1 hash is 0?

  18. SOLVED! What is the shortest set of consecutive NUL octets for which the 1024-bit FNV-1 hash is 0?

    NOTE: Russ Cox's solution below is for the set of 6 challenges immediately above

    General FNV solution by Russ Cox <rcs Email address> on 2011-Mar-02:
    There is no such stream of NUL octets.
    
    Xor with an odd byte flips the parity of the hash.
    Xor with an even byte leaves it alone, as does multiplying
    by any of the (odd) FNV primes. Thus the final hash has
    the same parity as the initial offset if and only if there
    are an even number of odd bytes in the input. This is
    the reason that all the offset bases have the same parity
    (odd, it turns out), and it implies that any consecutive
    stream of NULs will have an odd (non-zero) hash.
    

  19. SOLVED! What is the shortest set of consecutive NUL octets for which the 32-bit FNV-1a hash is 0?

  20. SOLVED! What is the shortest set of consecutive NUL octets for which the 64-bit FNV-1a hash is 0?

  21. SOLVED! What is the shortest set of consecutive NUL octets for which the 128-bit FNV-1a hash is 0?

  22. SOLVED! What is the shortest set of consecutive NUL octets for which the 256-bit FNV-1a hash is 0?

  23. SOLVED! What is the shortest set of consecutive NUL octets for which the 512-bit FNV-1a hash is 0?

  24. SOLVED! What is the shortest set of consecutive NUL octets for which the 1024-bit FNV-1a hash is 0?

    NOTE: Russ Cox's solution below is for the set of 6 challenges immediately above

    General FNV solution by Russ Cox <rcs Email address> on 2011-Mar-02:
    There is no such stream of NUL octets.
    
    Xor with an odd byte flips the parity of the hash.
    Xor with an even byte leaves it alone, as does multiplying
    by any of the (odd) FNV primes. Thus the final hash has
    the same parity as the initial offset if and only if there
    are an even number of odd bytes in the input. This is
    the reason that all the offset bases have the same parity
    (odd, it turns out), and it implies that any consecutive
    stream of NULs will have an odd (non-zero) hash.
    

    NOTE: By set of consecutive NUL octets we mean consecutive octets of 0 value.

  25. SOLVED! What is the shortest set of consecutive 0xff octets for which the 32-bit FNV-1 hash is 0?
    32-bit solution by Russ Cox <rcs Email address> on 2011-Mar-02:
    428876705 0xff octets.

    Peter de Rivaz <peter.derivaz Email address> independently confirmed this result.

    Richard Heylen <richard_in_reading Email address> independently confirmed this result.

  26. SOLVED! What is the shortest set of consecutive 0xff octets for which the 64-bit FNV-1 hash is 0?
    64-bit solution by Peter de Rivaz <peter.derivaz Email address> on 2011-Dec-13:
    9896220416391497057 0xff octets.

    Richard Heylen <richard_in_reading Email address> independently confirmed this result.

  27. SOLVED! What is the shortest set of consecutive 0xff octets for which the 128-bit FNV-1 hash is 0?
    128-bit solution by Richard Heylen <richard_in_reading Email address> on 2011-Dec-14:
    152812075112152085146780705563019820097 0xff octets.

    Peter de Rivaz <peter.derivaz Email address> independently confirmed this result.

  28. SOLVED! What is the shortest set of consecutive 0xff octets for which the 256-bit FNV-1 hash is 0?
    256-bit solution by Richard Heylen <richard_in_reading Email address> on 2011-Dec-14:
    971310111339922874984865931636119693708047768520568964839262806324177446
    08641 0xff octets.

    Peter de Rivaz <peter.derivaz Email address> independently confirmed this result.

  29. SOLVED! What is the shortest set of consecutive 0xff octets for which the 512-bit FNV-1 hash is 0?
    512-bit solution by Richard Heylen <richard_in_reading Email address> on 2011-Dec-14:
    612806956068056576215461080927099484400241024395026354420378459322301684
    399722907408508285157251830003265846176457230616192353760639874361657361
    1559921729 0xff octets.

    Peter de Rivaz <peter.derivaz Email address> independently confirmed this result.

  30. Partial solution: What is the shortest set of consecutive 0xff octets for which the 1024-bit FNV-1 hash is 0?
    Richard Heylen <richard_in_reading Email address> on 2011-Dec-14 found a 1024-bit solution, one that may not be the shortest:
    416676424643376760772449487657397580462250574503060952762179226758571093
    761689059455392577969506880247688215845019822014535567311051405867916840
    497646798425786609620276239990874926250263846724497488057368971095038212
    934393820920453733216924021449681744199270750560657371464991242494173425
    0024772314731200245 0xff octets.

    Peter de Rivaz <peter.derivaz Email address> independently confirmed this partial solution.

    NOTE: Russ Cox <rcs Email address> also observed that as a consequence of his solution to the consecutive NUL octet challences, any consecutive stream of 0xff with a zero FNV-1 or FNV-1a hash of any size must be of odd length.

  31. SOLVED! What is the shortest set of consecutive 0xff octets for which the 32-bit FNV-1a hash is 0?
    32-bit solution by Russ Cox <rcs Email address> on 2011-Mar-02:
    3039744951 0xff octets.

    Peter de Rivaz <peter.derivaz Email address> independently confirmed this result.

    Richard Heylen <richard_in_reading Email address> independently confirmed this result.

  32. Partial solution: What is the shortest set of consecutive 0xff octets for which the 64-bit FNV-1a hash is 0?
    Peter de Rivaz <peter.derivaz Email address> on 2011-Dec-13 found a 64-bit solution that may not be the shortest:
    5125902172520635575 0xff octets.

    Richard Heylen <richard_in_reading Email address> independently confirmed this partial solution.

  33. Partial solution: What is the shortest set of consecutive 0xff octets for which the 128-bit FNV-1a hash is 0?
    Peter de Rivaz <peter.derivaz Email address> on 2012-Mar-22 found a 128-bit solution that may not be the shortest:
    195988526173479582814801599910495893127 0xff octets.

    Richard Heylen <richard_in_reading Email address> independently confirmed this partial solution.

  34. Partial solution: What is the shortest set of consecutive 0xff octets for which the 256-bit FNV-1a hash is 0?
    Peter de Rivaz <peter.derivaz Email address> on 2012-Mar-22 found a 256-bit solution that may not be the shortest:
    121365261308607922778298441917362349745681574069429011964286973126957522
    07543 0xff octets.

    Richard Heylen <richard_in_reading Email address> independently confirmed this partial solution.

  35. Partial solution: What is the shortest set of consecutive 0xff octets for which the 512-bit FNV-1a hash is 0?
    Peter de Rivaz <peter.derivaz Email address> on 2012-Mar-22 found a 512-bit solution that may not be the shortest:
    445359075217293949446034810045247904893303946817563293272717969680141569
    129699002471949546033702514868111823565737421304575683326671821385410536
    5691076111 0xff octets.

    Richard Heylen <richard_in_reading Email address> independently confirmed this partial solution.

  36. Partial solution: What is the shortest set of consecutive 0xff octets for which the 1024-bit FNV-1a hash is 0?
    Peter de Rivaz <peter.derivaz Email address> on 2012-Mar-22 found a 1024-bit solution that may not be the shortest:
    712131032390661212423469446429778580303529367161714287727915539272088837
    388997682828851224650621762650604398414532544740385461220466517818153731
    651665570936392160298954932547331005615954561744064764751259871084045735
    302812555692177957250787849447135140298017119914349292668850620197682629
    52245579219890855775 0xff octets.

    Richard Heylen <richard_in_reading Email address> independently confirmed this partial solution.

    NOTE: Russ Cox <rcs Email address> observed that as a consequence of his solution to the consecutive NUL octet challences, any consecutive stream of 0xff with a zero FNV-1 or FNV-1a hash of any size must be of odd length.

    NOTE: By set of consecutive 0xff octets we mean consecutive octets of 0xff value.

  37. SOLVED! What is the shortest non-NUL ASCII string for which the 32-bit FNV-1 hash is 0?
    32-bit solution by Russ Cox <rcs Email address> on 2011-Mar-02:
    The solutions of length 5 are:
    
    FNV32_1(07 65 76 4a 3b) = 0    \a e v J ;
    FNV32_1(27 0f 56 47 0a) = 0    ' ^O V G \n
    FNV32_1(30 17 22 62 62) = 0    0 ^W " b b
    FNV32_1(30 33 53 42 5b) = 0    0 3 S B [
    FNV32_1(54 20 75 7b 5b) = 0    T space u { [
    FNV32_1(62 61 2c 31 71) = 0    b a , 1 q
    

  38. SOLVED! What is the shortest non-NUL ASCII string for which the 64-bit FNV-1 hash is 0?
    64-bit solution by Peter de Rivaz <peter.derivaz Email address> on 2011-Mar-11:
    The shortest solution is of length 10:
    
    FNV64_1(10 17 34 7c 28 61 38 72 64 4d) = 0    ^P ^H 4 ! ( a 8 r d M
    
    While there are other solutions of length 10, there are no solutions shorter
    than length 10.
    

  39. What is the shortest non-NUL ASCII string for which the 128-bit FNV-1 hash is 0?

  40. What is the shortest non-NUL ASCII string for which the 256-bit FNV-1 hash is 0?

  41. What is the shortest non-NUL ASCII string for which the 512-bit FNV-1 hash is 0?

  42. What is the shortest non-NUL ASCII string for which the 1024-bit FNV-1 hash is 0?

  43. SOLVED! What is the shortest non-NUL ASCII string for which the 32-bit FNV-1a hash is 0?
    32-bit solution by Russ Cox <rcs Email address> on 2011-Mar-02:
    The solutions of length 5 are:
    
    FNV32_1a(12 3b 5b 23 20) = 0    ^R ; [ # space
    FNV32_1a(2b 21 3d 79 47) = 0    + ! = y G
    FNV32_1a(2f 06 3c 37 71) = 0    / ^F < 7 q
    FNV32_1a(36 38 6d 2a 20) = 0    6 8 m * space
    FNV32_1a(40 24 1b 38 42) = 0    @ $ Esc 8 B
    FNV32_1a(4c 39 59 56 11) = 0    L 9 Y V ^Q
    FNV32_1a(59 08 26 60 62) = 0    Y \b & ` b
    FNV32_1a(60 4a 63 6f 11) = 0    ` J c o ^Q
    FNV32_1a(65 53 4e 2e 31) = 0    e S N . 1
    

  44. What is the shortest non-NUL ASCII string for which the 64-bit FNV-1a hash is 0?

  45. What is the shortest non-NUL ASCII string for which the 128-bit FNV-1a hash is 0?

  46. What is the shortest non-NUL ASCII string for which the 256-bit FNV-1a hash is 0?

  47. What is the shortest non-NUL ASCII string for which the 512-bit FNV-1a hash is 0?

  48. What is the shortest non-NUL ASCII string for which the 1024-bit FNV-1a hash is 0?

    NOTE: By non-NUL ASCII string we mean any arbitrary collection of non-NUL ASCII 8-bit characters in the range: [0x01 - 0x7f]. Obviously the C-style terminating NUL octet is not included.

  49. SOLVED! What is the shortest printable ASCII string for which the 32-bit FNV-1 hash is 0?
    32-bit hash solution by Russ Cox <rcs Email address> on 2011-Mar-02:
    The solutions of length 5 are:
    
    FNV32_1(30 33 53 42 5b) = 0    0 3 S B [
    FNV32_1(54 20 75 7b 5b) = 0    T Space u { [
    FNV32_1(62 61 2c 31 71) = 0    b a , 1 q
    

  50. What is the shortest printable ASCII string for which the 64-bit FNV-1 hash is 0?

  51. What is the shortest printable ASCII string for which the 128-bit FNV-1 hash is 0?

  52. What is the shortest printable ASCII string for which the 256-bit FNV-1 hash is 0?

  53. What is the shortest printable ASCII string for which the 512-bit FNV-1 hash is 0?

  54. What is the shortest printable ASCII string for which the 1024-bit FNV-1 hash is 0?

  55. SOLVED! What is the shortest printable ASCII string for which the 32-bit FNV-1a hash is 0?
    32-bit hash solution by Russ Cox <rcs Email address> on 2011-Mar-02:
    The solutions of length 5 are:
    
    FNV32_1a(2b 21 3d 79 47) = 0    + ! = y G
    FNV32_1a(36 38 6d 2a 20) = 0    6 8 m * Space
    FNV32_1a(65 53 4e 2e 31) = 0    e S N . 1
    

  56. What is the shortest printable ASCII string for which the 64-bit FNV-1a hash is 0?

  57. What is the shortest printable ASCII string for which the 128-bit FNV-1a hash is 0?

  58. What is the shortest printable ASCII string for which the 256-bit FNV-1a hash is 0?

  59. What is the shortest printable ASCII string for which the 512-bit FNV-1a hash is 0?

  60. What is the shortest printable ASCII string for which the 1024-bit FNV-1a hash is 0?

    NOTE: By printable ASCII string we mean any arbitrary collection of printable ASCII 8-bit characters in the range: [0x20 - 0x7e]. Obviously the C-style terminating NUL octet is not included.

  61. SOLVED! What is the shortest alphanumeric ASCII string for which the 32-bit FNV-1 hash is 0?
    32-bit hash solution by Russ Cox <rcs Email address> on 2011-Mar-02:
    The solutions of length 6 are:
    
    
    FNV32_1(33 64 37 41 35 4b) = 0    3 d 7 A 5 K
    FNV32_1(39 71 36 4d 71 33) = 0    9 q 6 M q 3
    FNV32_1(48 48 59 53 4c 45) = 0    H H Y S L E
    FNV32_1(54 72 4c 64 5a 31) = 0    T r L d Z 1
    FNV32_1(56 4c 33 42 71 43) = 0    V L 3 B q C
    FNV32_1(57 41 64 32 60 57) = 0    W A d 2 ` W
    FNV32_1(59 55 6f 31 39 6c) = 0    Y U o 1 9 l
    FNV32_1(59 66 36 68 50 36) = 0    Y f 6 h P 6
    FNV32_1(68 49 72 6a 46 6a) = 0    h I r j F j
    FNV32_1(6e 60 62 76 33 52) = 0    n ` b v 3 R
    FNV32_1(70 6c 49 7a 6c 60) = 0    p l I z l `
    FNV32_1(75 4d 6b 60 39 51) = 0    u M k ` 9 Q
    FNV32_1(79 73 6f 70 48 6c) = 0    y s o p H l
    FNV32_1(7a 63 49 6b 43 65) = 0    z c I k C e
    

  62. What is the shortest alphanumeric ASCII string for which the 64-bit FNV-1 hash is 0?

  63. What is the shortest alphanumeric ASCII string for which the 128-bit FNV-1 hash is 0?

  64. What is the shortest alphanumeric ASCII string for which the 256-bit FNV-1 hash is 0?

  65. What is the shortest alphanumeric ASCII string for which the 512-bit FNV-1 hash is 0?

  66. What is the shortest alphanumeric ASCII string for which the 1024-bit FNV-1 hash is 0?

  67. SOLVED! What is the shortest alphanumeric ASCII string for which the 32-bit FNV-1a hash is 0?
    32-bit hash solution by Russ Cox <rcs Email address> on 2011-Mar-02:
    The solutions of length 6 are:
    
    FNV32_1a(33 70 6a 4e 71 4d) = 0    3 p j N q M
    FNV32_1a(35 52 30 4c 67 37) = 0    5 R 0 L g 7
    FNV32_1a(37 6f 45 34 38 36) = 0    7 o E 4 8 6
    FNV32_1a(42 52 34 32 71 66) = 0    B R 4 2 q f
    FNV32_1a(46 6f 75 42 53 72) = 0    F o u B S r
    FNV32_1a(47 6b 6b 7a 46 44) = 0    G k k z F D
    FNV32_1a(48 56 47 5a 71 39) = 0    H V G Z q 9
    FNV32_1a(49 77 50 53 64 54) = 0    I w P S d T
    FNV32_1a(60 6e 72 59 33 47) = 0    ` n r Y 3 G
    FNV32_1a(71 7a 73 30 55 44) = 0    q z s 0 U D
    FNV32_1a(73 58 62 73 73 72) = 0    s X b s s r
    FNV32_1a(75 68 34 74 53 49) = 0    u h 4 t S I
    

  68. What is the shortest alphanumeric ASCII string for which the 64-bit FNV-1a hash is 0?

  69. What is the shortest alphanumeric ASCII string for which the 128-bit FNV-1a hash is 0?

  70. What is the shortest alphanumeric ASCII string for which the 256-bit FNV-1a hash is 0?

  71. What is the shortest alphanumeric ASCII string for which the 512-bit FNV-1a hash is 0?

  72. What is the shortest alphanumeric ASCII string for which the 1024-bit FNV-1a hash is 0?

    NOTE: By alphanumeric ASCII string we mean any arbitrary collection of alphanumeric ASCII 8-bit characters in the range: [0x30 - 0x39, 0x41 - 0x5a, 0x60 - 0x7a] Obviously the C-style terminating NUL octet is not included.



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