I tested some different algorithms, measuring speed and number of collisions.
I used three different key sets:
A list of 216,553 English words (in lowercase)
The numbers “1” to “216553” (think ZIP codes, and how a poor hash took down msn.com)
216,553 “random” (i.e. type 4 uuid) GUIDs
For each corpus, the number of collisions and the average time spent hashing was recorded.
I tested:
DJB2
DJB2a (variant using xor rather than +)
FNV-1 (32-bit)
FNV-1a (32-bit)
SDBM
CRC32
Murmur2 (32-bit)
SuperFastHash
Results
Each result contains the average hash time, and the number of collisions
Hash Lowercase Random UUID Numbers
============= ============= =========== ==============
Murmur 145 ns 259 ns 92 ns
6 collis 5 collis 0 collis
FNV-1a 152 ns 504 ns 86 ns
4 collis 4 collis 0 collis
FNV-1 184 ns 730 ns 92 ns
1 collis 5 collis 0 collis▪
DBJ2a 158 ns 443 ns 91 ns
5 collis 6 collis 0 collis▪▪▪
DJB2 156 ns 437 ns 93 ns
7 collis 6 collis 0 collis▪▪▪
SDBM 148 ns 484 ns 90 ns
4 collis 6 collis 0 collis**
SuperFastHash 164 ns 344 ns 118 ns
85 collis 4 collis 18742 collis
CRC32 250 ns 946 ns 130 ns
2 collis 0 collis 0 collis
LoseLose 338 ns – –
215178 collis
Notes:
The LoseLose algorithm (where hash = hash+character) is truly awful. Everything collides into the same 1,375 buckets
SuperFastHash is fast, with things looking pretty scattered; by my goodness the number collisions. I’m hoping the guy who ported it got something wrong; it’s pretty bad
CRC32 is pretty good. Slower, and a 1k lookup table
Do collisions actually happen?
Yes. I started writing my test program to see if hash collisions actually happen – and are not just a theoretical construct. They do indeed happen:
FNV-1 collisions
creamwove collides with quists
FNV-1a collisions
costarring collides with liquid
declinate collides with macallums
altarage collides with zinke
altarages collides with zinkes
Murmur2 collisions
cataract collides with periti
roquette collides with skivie
shawl collides with stormbound
dowlases collides with tramontane
cricketings collides with twanger
longans collides with whigs
DJB2 collisions
hetairas collides with mentioner
heliotropes collides with neurospora
depravement collides with serafins
stylist collides with subgenera
joyful collides with synaphea
redescribed collides with urites
dram collides with vivency
DJB2a collisions
haggadot collides with loathsomenesses
adorablenesses collides with rentability
playwright collides with snush
playwrighting collides with snushing
treponematoses collides with waterbeds
CRC32 collisions
codding collides with gnu
exhibiters collides with schlager
SuperFastHash collisions
dahabiah collides with drapability
encharm collides with enclave
grahams collides with gramary
…snip 79 collisions…
night collides with vigil
nights collides with vigils
finks collides with vinic
Randomnessification
The other subjective measure is how randomly distributed the hashes are. Mapping the resulting HashTables shows how evenly the data is distributed. All the hash functions show good distribution when mapping the table linearly:
Enter image description here
Or as a Hilbert Map (XKCD is always relevant):
Enter image description here
Except when hashing number strings (“1”, “2”, …, “216553”) (for example, zip codes), where patterns begin to emerge in most of the hashing algorithms:
SDBM:
Enter image description here
DJB2a:
Enter image description here
FNV-1:
Enter image description here
All except FNV-1a, which still look plenty random to me:
Enter image description here
In fact, Murmur2 seems to have even better randomness with Numbers than FNV-1a:
Enter image description here
When I look at the FNV-1a “number” map, I think I see subtle vertical patterns. With Murmur I see no patterns at all. What do you think?
The extra * in the above table denotes how bad the randomness is. With FNV-1a being the best, and DJB2x being the worst:
Murmur2: .
FNV-1a: .
FNV-1: ▪
DJB2: ▪▪
DJB2a: ▪▪
SDBM: ▪▪▪
SuperFastHash: .
CRC: ▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
Loselose: ▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
▪
▪▪▪▪▪▪▪▪▪▪▪▪▪
▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
I originally wrote this program to decide if I even had to worry about collisions: I do.
And then it turned into making sure that the hash functions were sufficiently random.
FNV-1a algorithm
The FNV1 hash comes in variants that return 32, 64, 128, 256, 512 and 1024 bit hashes.
The FNV-1a algorithm is:
hash = FNV_offset_basis
for each octetOfData to be hashed
hash = hash xor octetOfData
hash = hash * FNV_prime
return hash
Where the constants FNV_offset_basis and FNV_prime depend on the return hash size you want:
Hash Size Prime Offset
=========== =========================== =================================
32-bit 16777619 2166136261
64-bit 1099511628211 14695981039346656037
128-bit 309485009821345068724781371 144066263297769815596495629667062367629
256-bit
prime: 2^168 + 2^8 + 0x63 = 374144419156711147060143317175368453031918731002211
offset: 100029257958052580907070968620625704837092796014241193945225284501741471925557
512-bit
prime: 2^344 + 2^8 + 0x57 = 35835915874844867368919076489095108449946327955754392558399825615420669938882575126094039892345713852759
offset: 9659303129496669498009435400716310466090418745672637896108374329434462657994582932197716438449813051892206539805784495328239340083876191928701583869517785
1024-bit
prime: 2^680 + 2^8 + 0x8d = 5016456510113118655434598811035278955030765345404790744303017523831112055108147451509157692220295382716162651878526895249385292291816524375083746691371804094271873160484737966720260389217684476157468082573
offset: 1419779506494762106872207064140321832088062279544193396087847491461758272325229673230371772250864096521202355549365628174669108571814760471015076148029755969804077320157692458563003215304957150157403644460363550505412711285966361610267868082893823963790439336411086884584107735010676915
See the main FNV page for details.
As a practical matter:
32-bit UInt32,
64-bit UInt64, and
128-bit Guid can be useful
All my results are with the 32-bit variant.
FNV-1 better than FNV-1a?
No. FNV-1a is all around better. There was more collisions with FNV-1a when using the English word corpus:
Hash Word Collisions
====== ===============
FNV-1 1
FNV-1a 4
Now compare lowercase and uppercase:
Hash lowercase word Collisions UPPERCASE word collisions
====== ========================= =========================
FNV-1 1 9
FNV-1a 4 11
In this case FNV-1a isn’t “400%” worse than FN-1, only 20% worse.
I think the more important takeaway is that there are two classes of algorithms when it comes to collisions:
collisions rare: FNV-1, FNV-1a, DJB2, DJB2a, SDBM
collisions common: SuperFastHash, Loselose
And then there’s the how evenly distributed the hashes are:
outstanding distribution: Murmur2, FNV-1a, SuperFastHas
excellent distribution: FNV-1
good distribution: SDBM, DJB2, DJB2a
horrible distribution: Loselose
Update
Murmur? Sure, why not
Update
@whatshisname wondered how a CRC32 would perform, added numbers to the table.
CRC32 is pretty good. Few collisions, but slower, and the overhead of a 1k lookup table.
Snip all erroneous stuff about CRC distribution – my bad
Up until today I was going to use FNV-1a as my de facto hash-table hashing algorithm. But now I’m switching to Murmur2:
Faster
Better randomnessification of all classes of input
And I really, really hope there’s something wrong with the SuperFastHash algorithm I found; it’s too bad to be as popular as it is.
Update: From the MurmurHash3 homepage on Google:
(1) – SuperFastHash has very poor collision properties, which have been documented elsewhere.
So I guess it’s not just me.
Update: I realized why Murmur is faster than the others. MurmurHash2 operates on four bytes at a time. Most algorithms are byte by byte:
for each octet in Key
AddTheOctetToTheHash
This means that as keys get longer Murmur gets its chance to shine.
Update
GUIDs are designed to be unique, not random
A timely post by Raymond Chen reiterates the fact that “random” GUIDs are not meant to be used for their randomness. They, or a subset of them, are unsuitable as a hash key:
Even the Version 4 GUID algorithm is not guaranteed to be unpredictable, because the algorithm does not specify the quality of the random number generator. The Wikipedia article for GUID contains primary research which suggests that future and previous GUIDs can be predicted based on knowledge of the random number generator state, since the generator is not cryptographically strong.
Randomess is not the same as collision avoidance; which is why it would be a mistake to try to invent your own “hashing” algorithm by taking some subset of a “random” guid:
int HashKeyFromGuid(Guid type4uuid)
{
//A “4” is put somewhere in the GUID.
//I can’t remember exactly where, but it doesn’t matter for
//the illustrative purposes of this pseudocode
int guidVersion = ((type4uuid.D3 & 0x0f00) >> 8);
Assert(guidVersion == 4);
return (int)GetFirstFourBytesOfGuid(type4uuid);
}
Note: Again, I put “random GUID” in quotes, because it’s the “random” variant of GUIDs. A more accurate description would be Type 4 UUID. But nobody knows what type 4, or types 1, 3 and 5 are. So it’s just easier to call them “random” GUIDs.
All English Words mirrors
http://www.filedropper.com/allenglishwords
https://web.archive.org/web/20070221060514/http://www.sitopreferito.it/html/all_english_words.html
shareimprove this answer
edited Nov 9 ’15 at 18:12
answered Apr 23 ’12 at 12:42
Ian Boyd
12.6k1911
181
some of the collisions make awesome band names. Particularly ‘Adorable Rentability’ – mcfinnigan Apr 23 ’12 at 14:35
27
Also, I’d love to hear how you generated these results (source code and/or tools) – Earlz Apr 23 ’12 at 17:40
32
@Earlz Development tool is Delphi. i assume you mean the images though. For “linear” map i created a square bitmap of size nxn, (where n = Ceil(sqrt(hashTable.Capacity))). Rather than simply black for list entry is occupied and white for list entry is empty, i used an HSLtoRGB function, where the hue ranged from 0 (red) to 300 (magenta). White is still an “empty list cell”. For the Hilbert map i had to hunt wikipedia for the algorithm that turns an index into an (x,y) coordinate. – Ian Boyd Apr 23 ’12 at 18:15
32
I’ve removed a number of comments that were along the lines of “+1 great answer!” – Please don’t post comments that don’t ask for clarifications or add information to the answer, if you feel it’s a great answer, upvote it 😉 – Yannis♦ Apr 28 ’12 at 20:34
11
It would be really interesting to see how SHA compares, not because it’s a good candidate for a hashing algorithm here but it would be really interesting to see how any cryptographic hash compares with these made for speed algorithms. – Michael May 25 ’12 at 15:09
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up vote 30 down vote
Here is a list of hash functions, but the short version is:
If you just want to have a good hash function, and cannot wait, djb2 is one of the best string hash functions i know. It has excellent distribution and speed on many different sets of keys and table sizes
unsigned long
hash(unsigned char *str)
{
unsigned long hash = 5381;
int c;
while (c = *str++)
hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
return hash;
}
shareimprove this answer
answered Feb 19 '11 at 1:13
Dean Harding
17.8k33967
2
Actually djb2 is zero sensitive, as most such simple hash functions, so you can easily break such hashes. It has a bad bias too many collisions and a bad distribution, it breaks on most smhasher quality tests: See github.com/rurban/smhasher/blob/master/doc/bernstein His cdb database uses it, but I wouldn't use it with public access. – rurban Aug 20 '14 at 6:03
add a comment
up vote 26 down vote
If you are wanting to create a hash map from an unchanging dictionary, you might want to consider perfect hashing https://en.wikipedia.org/wiki/Perfect_hash_function – during the construction of the hash function and hash table, you can guarantee, for a given dataset, that there will be no collisions.
shareimprove this answer
answered May 25 '12 at 3:16
Damien
26132
4
+1 I wasn't aware of such an algorithm – Earlz May 25 '12 at 5:00
2
Here's more about (minimal) Perfect Hashing burtleburtle.net/bob/hash/perfect.html including performance data, although it doesn't use the most current processor etc. – Ellie Kesselman May 29 '12 at 12:24
3
It's pretty obvious, but worth pointing out that in order to guarantee no collisions, the keys would have to be the same size as the values, unless there are constraints on the values the algorithm can capitalize on. – devios Apr 4 '13 at 20:34
I improved gperf and provide a nice frontend to most perfect hash generators at github.com/rurban/Perfect-Hash It's not yet finished, but already better then the existing tools. – rurban Aug 20 '14 at 6:05
@devios: I've recently learned that there are several hash table algorithms that guarantee no collisions, even when you use long strings as keys, strings much longer than the hash table index values generated by the hash function, without any constraints on those strings. See cs.stackexchange.com/questions/477/… . – David Cary Jun 8 '15 at 17:11
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up vote 20 down vote
CityHash by Google is the algorithm you are looking for. It is not good for cryptography but is good for generating unique hashes.
Read the blog for more details and the code is available here.
CityHash is written in C++. There also is a plain C port.
About 32-bit support:
All the CityHash functions are tuned for 64-bit processors. That said, they will run (except for the new ones that use SSE4.2) in 32-bit code. They won't be very fast though. You may want to use Murmur or something else in 32-bit code.
shareimprove this answer
edited May 29 '12 at 11:56
JanX2
1051
answered May 25 '12 at 10:29
Vipin Parakkat
30924
6
Is CityHash pronounced similar to "City Sushi?" – Eric Mar 20 '13 at 21:20
Have a look at SipHash too, it is meant to replace MurmurHash/CityHash/etc. : 131002.net/siphash – Török Edwin Oct 15 '13 at 8:47
1
Also see FarmHash, a successor to CitHash. code.google.com/p/farmhash – stevendaniels Mar 18 '15 at 13:15
1
xxHash claims to be 5x faster than CityHash. – Clay Bridges May 22 '15 at 15:56
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up vote 12 down vote
The SHA algorithms (including SHA-256) are designed to be fast.
In fact, their speed can be a problem sometimes. In particular, a common technique for storing a password-derived token is to run a standard fast hash algorithm 10,000 times (storing the hash of the hash of the hash of the hash of the … password).
#!/usr/bin/env ruby
require 'securerandom'
require 'digest'
require 'benchmark'
def run_random_digest(digest, count)
v = SecureRandom.random_bytes(digest.block_length)
count.times { v = digest.digest(v) }
v
end
Benchmark.bmbm do |x|
x.report { run_random_digest(Digest::SHA256.new, 1_000_000) }
end
Output:
Rehearsal ————————————
1.480000 0.000000 1.480000 ( 1.391229)
————————— total: 1.480000sec
user system total real
1.400000 0.000000 1.400000 ( 1.382016)
shareimprove this answer
answered Feb 19 '11 at 0:21
yfeldblum
1,32579
36
It's relatively fast, sure, for a cryptographic hashing algorithm. But the OP just wants to store values in a hashtable, and I don't think a cryptographic hash function is really appropriate for that. – Dean Harding Feb 19 '11 at 1:10
6
The question brought up (tangentially, it now appears) the subject of the cryptographic hash functions. That's the bit I am responding to. – yfeldblum Feb 22 '11 at 13:14
7
Just to put people off the idea of "In particular, a common technique for storing a password-derived token is to run a standard fast hash algorithm 10,000 times" — while common, that's just plain stupid. There are algorithms designed for these scenarios, e.g., bcrypt. Use the right tools. – TC1 Oct 14 '13 at 13:19
1
Cryptographic hashes are designed to have a high throughput, but that often means they have high setup, teardown, .rodata and/or state costs. When you want an algorithm for a hashtable, you usually have very short keys, and lots of them, but do not need the additional guarantees of a cryptographic has. I use a tweaked Jenkins’ one-at-a-time myself. – mirabilos Dec 6 '13 at 13:57
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up vote 9 down vote
I've plotted a short speed comparasion of different hashing algorithms when hashing files.
The individual plots only differ slightly in the reading method and can be ignored here, since all files were stored in a tmpfs. Therefore the benchmark was not IO-Bound if you are wondering.
Linear Scale
Logarithmic scale
Algorithms include: SpookyHash, CityHash, Murmur3, MD5, SHA{1,256,512}.
Conclusions:
Non-cryptographich hasfunctions like Murmur3, Cityhash and Spooky are pretty close together. One should note that Cityhash may be faster on CPUs with SSE 4.2s CRC instruction, which my CPU does not have. SpookyHash was in my case always a tiny bit before CityHash.
MD5 seems to be a good tradeoff when using cryptographic hashfunctions, although SHA256 may be more secure to the collision vulnerabilities of MD5 and SHA1.
The complexity of all algorithms is linear – which is really not surprising since they work blockwise. (I wanted to see if the reading method makes a difference, so you can just compare the rightmost values).
SHA256 was slower than SHA512.
I did not investigate the randomness of the hashfunctions. But here is a good comparasion of the hashfunctions that are missing in Ian Boyds answer. This points out that CityHash has some problems in corner cases.
The source used for the plots:
https://github.com/sahib/rmlint/tree/gh-pages/plots (sorry for the ugly code)
