From: Jacques Garrigue <garrigue@math.nagoya-u.ac.jp>
To: kamaradclimber@gmail.com
Cc: caml-list@inria.fr
Subject: Re: [Caml-list] range of hash function
Date: Sat, 20 Feb 2010 22:54:12 +0900 (JST) [thread overview]
Message-ID: <20100220.225412.98507853.garrigue@math.nagoya-u.ac.jp> (raw)
In-Reply-To: <1ae8fe881002200054s2e9752d8x620695c3c4e27939@mail.gmail.com>
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
architectures.
> 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
strings.
> 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
next prev parent reply other threads:[~2010-02-20 13:54 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-02-20 8:54 Grégoire Seux
2010-02-20 10:52 ` [Caml-list] " Goswin von Brederlow
2010-02-20 12:39 ` ygrek
2010-02-20 13:54 ` Jacques Garrigue [this message]
2010-02-21 23:10 ` Richard Jones
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