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range of hash function
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Date: 2010-02-20 (13:54)
From: Jacques Garrigue <garrigue@m...>
Subject: Re: [Caml-list] range of hash function
From: Grégoire Seux <kamaradclimber@gmail.com>
> i would like to use the polymorhpic hash function on strings. But i would
> like to know what is the probability of a collision between two hashes.
> my first question is about the range of the Hashtbl.hash function: what is
> its range ? ( string -> [1..N] ?)

Just to get things straight: this is 0..2^30-1 (0..0x3fffffff).
The result of the hash function is the same on 32-bit and 64-bit

> the second question is : can i assume that the result is a uniform
> distribution over [1..N] ? (for 10⁶ words which is an estimation of the
> english vocabulary size)

The algorithm for strings is as follows:

      i = caml_string_length(obj);
      for (p = &Byte_u(obj, 0); i > 0; i--, p++)
        hash_accu = hash_accu * 19 + *p;

So you can assume an uniform distribution for sufficiently long

> the third one is : is it possible to predict which will be the collision ? I
> mean collisions are between words which are very 'similar' (for ex: "boy"
> and "boys") or are completely unpredictable.

Since you have the algorithm, you can predict collisions. Basically
shifting character n by 1 is equivalent to shifting character n+1 by
19, so you have lots of collisions. But this hash function being
intended for hashtables, collisions are not a problem, uniform
distribution matters more.

By the way, for polymorphic variants collisions matter, and the hash
function is different. The range is 31-bits rather than 30-bits, and
the factor is 243, so that names of no more than 4 characters are
guaranteed to be different. You still have collisions, but they are
going to be less similar.

Both hash functions are defined in byterun/hash.c.

Hope this helps,

Jacques Garrigue