====== Hash Function Efficiency ======
(This article is also available [[hash:efficiency | in Russian]])

In article of Arash Partow
[[http://www.partow.net/programming/hashfunctions/ |
"General Purpose Hash Function Algorithms"]]
several 32-bit algorithms are reviewed:
  * rs --- simple hash function from Robert Sedgwicks book [[http://www.amazon.com/gp/product/0201514257/ | 'Algorithms in C']]
  * js --- bitwise hash function by Justin Sobel
  * pjw --- algorithm based on work by Peter J. Weinberger
  * bkdr --- hash function from Brian Kernighan and Dennis Ritchie's book [[http://www.amazon.com/gp/product/0131103628/ | 'The C Programming Language']]
  * sdbm --- algorithm of choice used in SDBM project
  * djb --- algorithm produced by Professor Daniel J. Bernstein
  * dek --- algorithm proposed by Donald E. Knuth in [[http://www.amazon.com/gp/product/0201896850/ | 'The Art Of Computer Programming']]
  * ap --- algorithm produced by Arash Partow

Another five variants:
  * faq6 --- number 6 from [[http://burtleburtle.net/bob/hash/hashfaq.html | FAQ by Bob Jenkins]]
  * lookup3 --- author [[http://burtleburtle.net/bob/hash/ | Bob Jenkins]]
  * ly --- proposed by [[http://leo.yuriev.ru/random | Leonid Yuriev]] (congruential generator)
  * rot13 --- simple algorithm with circular shift, by Serge Vakulenko
  * crc32 --- [[http://www.w3.org/TR/PNG-CRCAppendix.html | standard checksum]] with polynom x<sup>32</sup>+x<sup>26</sup>+x<sup>23</sup>+x<sup>22</sup>+x<sup>16</sup>+x<sup>12</sup>+x<sup>11</sup>+x<sup>10</sup>+x<sup>8</sup>+x<sup>7</sup>+x<sup>5</sup>+x<sup>4</sup>+x<sup>2</sup>+x+1

Here are [[sources | the C sources]].

===== Test 1 =====
To measure the efficiency of hash functions I prepared the following test data:
  * {{usdict.gz | American dictionary}} from Ispell project, 62075 words.
  * {{rudict.gz | Russian dictionary}} from Ispell project, 128900 words.
  * {{symbols.gz | A list of symbols}}, extracted from all libs on my linux workstation (libc.a and others), 136073 words.

Total volume after merging is **326797** different words.

For every word a 32-bit hash value was computed, and counted a number
of collisions.

^  Algorithm  ^  Collisions  ^
^  rs         |  9          |
^  js         |  98	    |
^  pjw        |  1315       |
^  bkdr       |  11	    |
^  sdbm       |  14	    |
^  djb        |  83	    |
^  dek        |  308        |
^  ap         |  16	    |
^  ly         |  9	    |
^  rot13      |  7	    |
^  faq6       |  14	    |
^  lookup3    |  9	    |
^  crc32      |  13	    |

A list of collisions for rs, bkdr, sdbm, ap, ly, rot13, faq6, lookup3 and crc32
is available [[conflicts | here]].

Algorithms with minimal collisions:
  * [[sources#ROT13 Hash Function| rot13]] --- one circular shift (rotation) and addition
  * [[sources#LOOKUP3 Hash Function| lookup3]] --- one shift and addition (or more)
  * [[sources#LY Hash Function| ly]] --- one multiplication and addition
  * [[sources#RS Hash Function| rs]] --- two multiplications

Results are presented on picture.
Two outsiders --- pjw and dek --- exceed the limits of Y axis.

{{hash-eff.png}}

----
===== Test 2 =====
In previous test, all data had MSB unchanged. For the second test another data set was selected:
  * {{dedict.gz | German dictionary}} from Ispell project, 39612 words.
  * {{hudict.gz | Hungarian dictionary}} from Ispell project, 211880 words.
  * {{itdict.gz | Italian dictionary}} from Ispell project, 37268 words.
  * {{sedict.gz | Swedish dictionary}} from Ispell project, 24019 words.

Total volume after merging is **310595** different words.

Algorithms js, pjw, djb и dek were excluded from testing.

^  Algorithm  ^  Collisions  ^
^  rs         |  5          |
^  bkdr       |  14	    |
^  sdbm       |  14	    |
^  ap         |  32	    |
^  ly         |  8	    |
^  rot13      |  10	    |
^  faq6       |  13	    |
^  lookup3    |  14	    |
^  crc32      |  15	    |

Algorithms with minimal collisions:
  * [[sources#RS Hash Function| rs]] --- two multiplications
  * [[sources#LY Hash Function| ly]] --- one multiplication and addition
  * [[sources#ROT13 Hash Function| rot13]] --- one circular shift (rotation) and addition

Results are presented on picture.

{{de-hu-se-it.png}}