Hash

A hash is a data structure. In Tcl, it is used for arrays, dicts, and many other things. For C programmers, the convenient and generic hash functions are one of the advantages of using the Tcl Portable Runtime Library.

A hash associates a value to each of zero or more keys, which are typically not sequential. The basic idea is to store the pairs of key and value in a vector (like a Tcl list), at a position computed by applying the hash function to the key. A good hash function thoroughly mixes the bits in the key and thereby produces a seemingly random number from each possible key. Chances are fairly good that no two keys in a particular hash get the same hash number, and then one can find the value corresponding to a key by computing its hash number and looking up the corresponding entry in the hash table vector.

Of course, sometimes two keys do get the same number, and then one need some strategy for handling such situations. Older literature often consider schemes for walking around the hash table vector until an empty entry is found an 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. Newer implementations rather tend to have each vector entry (a "bucket") be a pointer to a linked list of the key+value pairs that should fall in this entry.

Efficiency in hashes depend on having sufficiently many buckets that collisions don't happen too often, but having too many buckets is a waste of memory. Tcl hashes automatically adjust to the number of keys by occationally resizing themselves.

See also:

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.

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

Could someone please explain the "buckets with 0 entries" item? (RT 10Feb2010)

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.

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! - SPB

Category Concept	Category Data Structure