Problem: There are hash functions which are "good" in this sense, but they do not spread their randomness uniformly over the 32 bits.
Example: Integers use their own value as hash. This is ok, as far as the integers are uniformly distributed. But if they all contain a high power of two, for instance, the low bits give a very bad hash function.
Take a dictionary with integers range(1000) as keys and access all entries. Then use a dictionay with the integers shifted left by 16. Access time is slowed down by a factor of 100, since every access is a linear search now.
Ai. I think what happened is this: long ago, the hash table sizes were primes, or at least not powers of two! I'll leave it to the more mathematically-inclined to judge your solution... --Guido van Rossum (home page: http://www.python.org/~guido/)