> agreed that multiplication should be avoided. however, in some cases
> nothing else works.
However, this is not one of those cases, if loads are
much cheaper than multiplication. A quick
and easy hash function would be to hash a 20 bit
value by using its two 10 bit words as indices into
two tables of randomly chosen values (in the
range 0..PAGE_HASH_SIZE-1). Xor the two values together.
This class of hash functions (parameterized by
the table contents) is provably good, in the sense
that for any two distinct keys, a randomly chosen
hash function from this class will cause the keys
to collide with probability 1/PAGE_HASH_SIZE
(the class of hash functions is "universal";
see Cormen, Leiserson, and Rivest, "Introduction
to Algorithms", chapter 12.)
Moreover, the expected behavior of hashing with
chaining is O(n/m) time per operation for n values
stored in a table of size m (basically, pairwise
independence of the hash values is enough to
ensure this.) Again, this is regardless of
the actual keys; the randomness comes from the
tables.
Paul
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