python hash function

[Damien Morton]

Ive been doing some investigation of python hashtables and the hash
function used in Python.

It turns out, that when running pystone.py, as much time is spent in
string_hash() as is spent in lookdict_string(). If you look at
python's hash function, shown below, you can get an idea why - a
multiply is used for every character in the string.

static long
string_hash1(register char *p, int size)
{
	register int len;
	register long x;

	len = size;
	x = *p << 7;
	while (--len >= 0)
		x = (100003*x) ^ *p++;
	x ^= size;
	return x;
}

Looking around the web I found the following hash function, which is
much faster, and seems to distribute better than the python hash
function.

static long
string_hash3(register char *p, register int size)
{
	register long x;
	register char c;

	x = 0xd2d84a61;
        while (c = *p++)
		x ^= ( (x<<7) + c + (x>>5) );
	return x;
}

I also came up with a hash function of my own, which seems to
distribute near-perfectly (in the sense of being comparable to
assigning, as hashes, random numbers to unique strings) and be faster
yet (at least, on my P4 box).

static long
string_hash6(register unsigned short *p, int size)
{
	register short s;
	register unsigned long x = 0;

        if (size == 0) return 0;

	len = (size+1) >> 1;
	while (len--) {
		x += (x>>14) + (*p++ * 0xd2d84a61);
		}
	x += (x>>14) + (size*0xd2d84a61);
	
	return x;
}

Ive tested these functions by hashing a large set of strings generated
by instrumenting the python interpeter to emit a string every time a
string is added to a dictionary. These strings are hashed and thrown
into the buckets of various sized tables. I then calculate sigma
statistics (sum((observed-expected)^2)/(N-1)) for the number of items
in the buckets of those tables.

Im not sure what other tests to try out. Im hoping that someone on
c.l.py has some experience in testing hash functions, and can suggest
some additional tests and/or tweaks.