A hash is a value, deterministically produced by a hash function from its input value, that serves to segment values into groups. When there is nearly no chance that there will ever be more than one value in a group, the hash is called a signature. When the same hash is produced from two values, it is a collision.
A hash table is a data structure. In Tcl it is used for arrays, dictionaries, and many other things.
For C programmers, the Tcl Portable Runtime Library provides performant generic hash functions that support various types of keys, and are useful even if a project doesn't include a Tcl interpreter.
The hash of a value can be used to group values. A hash may have some clear relationship to the value it was derived from, or it may appear to have no relationship at all. It generally requires more effort to produce a hash that seems to be more random, and apparent lack of any relation to the input value is a requirement, a cryptographic hash, which must also be collision-resistant, and entirely unamenable to being deduced by any other means.
A hash can be used to quickly look up a key for a value: Hash each key and store all keys with the same hash together. When the value for a key is requested, hash the key to determine its group, scan through the group to find the stored key, and retrieve the value associated with it. This is how dictionaries and arrays are implemented. If the groups are getting overpopulated, switch to a hash function that provides more groups, and then move the existing data into the new groups.
A common way to store groups of values is as a linked list, a pointer to which is stored in an array which is used as the hash table. From time to time the number of buckets is adjusted to maintain both performance and storage efficiency. In Tcl, hash tables are automatically adjusted in this manner.
An older way of implementing a hash table is to store a value directly at the position indicated by its hash, and if that position is already occupied, to follow some strategy for handling the collision. Older literature often consider schemes for walking around the hash table vector until an empty entry is found and putting key+value pairs there when inserting; similarly one would when looking up a key have to walk ahead until finding an empty entry before concluding that the key wasn't in the hash. This approach makes the delete operation perilous, since replacing the deleted entry with an empty entry means that like-hashed entries past it can no longer be found. Thus there must be a "tombstone" entry which is empty in the sense that it can be overwritten but not empty in the sense that it doesn't terminate the chain.
DKF: The traditional hashing function used in Tcl is (abbreviated):
unsigned result = 0, ch;
for (ch=*string++ ; ch ; ch=*string++) {
result += (result<<3) + ch;
}
return result;That's not bad, because it both keeps the bits low down and mixes them up higher up.
In 8.6, we are trialling the FNV hash function instead:
unsigned result = 0x811c9dc5, ch;
#define FNV_32_PRIME ((unsigned) 0x01000193)
for (ch=*string++ ; ch ; ch=*string++) {
result = (result * FNV_32_PRIME) ^ ch;
}
return result;It seems to be a bit slower (not that the hash function is a bottleneck before or after) but it has impeccable credentials as a hash function. (The better ones are all much more complex.) Distribution results (i.e., the pattern of bucket chain lengths reported by array statistics) are inconclusive.
AMG: The referenced site recommends the alternative FNV-1a which XORs before multiplying:
result = (result ^ ch) * FNV_32_PRIME;
DKF: One benefit of the new algorithm is that it makes it trickier to create hash collisions. This code (thanks to Joe English) demonstrates:
proc collide {level {accum {}}} {
global a
if {$level} {
incr level -1
collide $level aj$accum
collide $level ba$accum
} else {
set a($accum) 1
}
}
puts [time {collide 15}]
puts [array statistics a]For 8.5, it produces this:
35404625 microseconds per iteration 32768 entries in table, 16384 buckets number of buckets with 0 entries: 16383 number of buckets with 1 entries: 0 number of buckets with 2 entries: 0 number of buckets with 3 entries: 0 number of buckets with 4 entries: 0 number of buckets with 5 entries: 0 number of buckets with 6 entries: 0 number of buckets with 7 entries: 0 number of buckets with 8 entries: 0 number of buckets with 9 entries: 0 number of buckets with 10 or more entries: 1 average search distance for entry: 16384.5
With the new function:
978683 microseconds per iteration 32768 entries in table, 16384 buckets number of buckets with 0 entries: 8345 number of buckets with 1 entries: 601 number of buckets with 2 entries: 1144 number of buckets with 3 entries: 1657 number of buckets with 4 entries: 1616 number of buckets with 5 entries: 1271 number of buckets with 6 entries: 848 number of buckets with 7 entries: 487 number of buckets with 8 entries: 237 number of buckets with 9 entries: 111 number of buckets with 10 or more entries: 67 average search distance for entry: 3.0
RT 2010-02-10: Could someone please explain the "buckets with 0 entries" item?
DKF: Sure. Tcl uses a hash scheme which assigns each key being hashed to a “bucket”, which is an array field that points to a linked list of “hash entries”. (Each entry holds the mapping from one key to one value.) When a bucket has no entries attached to it, it's empty; no keys are actually mapped to it. Sure, it's inefficient that there are empty buckets but it's not as terrible as all that; insisting that there are none is going towards perfect hashing, a different hashing scheme that typically requires deep knowledge of the keys – both quantity and format – being hashed to generate the hash function since it's vital with perfect hashing to have no collisions. Perfect hashing is totally unsuitable for the Tcl library as we don't want to constrain the keys at all.
The genius of hashing is that, providing the hash function generates a uniformly random distribution of hashcodes for the input keys, you can get a very efficient lookup scheme that avoids having to do a lot of comparisons or manage complex data structures like balanced trees. We don't get perfect distributions in practice of course (they require cryptographic hashing, which is relatively expensive) but the results are still Good Enough™ in most cases.
DKF: Also, Tcl's hashing is actually very good for numeric-string keys.
AMG: Unless I misunderstand the actual hash function being used, "19" and "20" have the same hash value. Many other collisions abound. This doesn't impact correctness, only performance. But consider also that "fixes" to this "problem" may have larger performance costs, so it's probably best to leave well enough alone.
SBP: My apologies if this is the wrong place, but I didn't think it deserved its own page... I am using a Tcl_HashTable in C to manage a collection of binary blobs, and I wish to efficiently get the number of blobs stored within the hash table (as a C integer). The header instructs me to "never access any fields in this structure", so accessing the numEntries field seems off limits. What is the proper way to determine the size of the hash table from C? Parsing the 'stats' string seems wrong. Thank you for any insight you share!
DKF: It's a little-advertised field of the Tcl_HashTable, which is a public data structure. In fact, it's probably the only externally-useful field of that structure (unless you're keen on estimating loading factors and stuff like that, which you probably should ignore).
Tcl_HashTable *hashTablePtr = ... /* get it from somewhere, OK? */ int size = hashTablePtr->numEntries;
Can't be much easier than that.