hashing an array - howto

[Helmut Jarausch]

Hi,

I need to hash arrays of integers (from the hash module).

So, I have to derive from array and supply a __hash__ method.
But how to hash an array (of fixed length, say 25)?
What I need is a function which maps a tuple of 25 integers
into 1 integer with good hashing properties.

Does anybody know such a thing?

Many thanks for a hint,

Helmut Jarausch

Lehrstuhl fuer Numerische Mathematik
RWTH - Aachen University
D 52056 Aachen, Germany

[Peter Otten]

Helmut Jarausch wrote:

I need to hash arrays of integers (from the hash module).

So, I have to derive from array and supply a __hash__ method.
But how to hash an array (of fixed length, say 25)?
What I need is a function which maps a tuple of 25 integers
into 1 integer with good hashing properties.

Does anybody know such a thing?

Have you tried this already?

def __hash__(self):
return hash(self.tostr ing())

Peter

[bearophileHUGS]

Helmut Jarausch:

I need to hash arrays of integers (from the hash module).

One of the possible solutions is to hash the equivalent tuple, but it
requires some memory (your sequence must not be tuples already):

assert not isinstance(some list, tuple)
hash(tuple(some list))

This is an alternative solution, it doesn't use much memory, but I am
not sure it works correctly:

from operator import xor
hash(reduce(xor , somelist))

Bye,
bearophile

[Michael Palmer]

On Sep 5, 11:18 am, bearophileH...@ lycos.com wrote:

Helmut Jarausch:

I need to hash arrays of integers (from the hash module).

One of the possible solutions is to hash the equivalent tuple, but it
requires some memory (your sequence must not be tuples already):

why can't it be tuple already? Doesn't matter:

>>from numpy import arange
a=arange(5)
a

array([0, 1, 2, 3, 4])

>>hash(a)

Traceback (most recent call last):
File "<stdin>", line 1, in ?
TypeError: unhashable type

>>b=tuple(a)
b

(0, 1, 2, 3, 4)

>>c=tuple(b)
c

(0, 1, 2, 3, 4)

>>hash(c)

1286958229

you can discard the tuple, so the memory requirement is transient.

[bearophileHUGS]

Michael Palmer:

why can't it be tuple already?

Because if the input list L has tuples and lists, they end having the
same hash value:

>>L = [[1,2,3], (1,2,3)]
hash(tuple( L[0])), hash(tuple(L[1]))

(-378539185, -378539185)

But it's a not much common situation, and few hash collision pairs
can't damage much, so I agree with you that my assert was useless.
This may solve that problem anyway:

hash(type(L)) ^ hash(tuple(L))

Generally a good hashing functions uses all the input information. If
you use tuple() you ignore part of the input information, that is the
type of L. So xor-ing hash(type(L)) you use that information too.

you can discard the tuple, so the memory requirement is transient.

Right, but there's lot of GC action, it may slow down the code. So you
can start using hash(tuple(L)), but if later the code performance
comes out bad, you may try a different version that creates less
intermediate garbage.

Bye,
bearophile

[bearophileHUGS]

John Machin:

Consider this:>>hash(123 ) == hash(123.0) == hash(123L)
True

Right... Can you explain me why Python designers have chosen to build
a hash() like that?

Try "uses all the information that is relevant to the task".

My knowledge of hash data structures seems not enough to understand
why.

Your alternative solution using reduce and xor may have suboptimal
characteristics ...

Right, sorry.

Bye,
bearophile

[John Machin]

On Sep 6, 7:49*am, bearophileH...@ lycos.com wrote:

John Machin:

Consider this:>>hash(123 ) == hash(123.0) == hash(123L)
True

Right... Can you explain me why Python designers have chosen to build
a hash() like that?

I can't channel them; my rationalisation is this:

Following the Law of Least Astonishment,

>123 == 123.0 == 123L

True

Consequently if x == y, then adict[x] and adict[y] should give the
same result.

Cheers,
John

[John Machin]

On Sep 6, 9:30*am, John Machin <sjmac...@lexic on.netwrote:

On Sep 6, 7:49*am, bearophileH...@ lycos.com wrote:

John Machin:

Consider this:>>hash(123 ) == hash(123.0) == hash(123L)
True

Right... Can you explain me why Python designers have chosen to build
a hash() like that?

I can't channel them; my rationalisation is this:

Following the Law of Least Astonishment,>1 23 == 123.0 == 123L

True

Consequently if x == y, then adict[x] and adict[y] should give the
same result.

Another reason for not folding in the type of the object is this:

>>type([])

<type 'list'>

>>hash(type([]))

505252536

>>id(type([]))

505252536

IOW hash(T) == id(T) where T is a type. id(obj) is just a memory
address which can vary between executions of the same Python binary on
the same machine ... not very reproducible. There is no guarantee in
the docs for hash about under what circumstances hash(x) != hash(x) of
course; I'm just relying on the least astonishment law again :-)

And, again, we don't know what the OP's full requirements are ...

[sudhi.herle]

On Sep 5, 9:38*am, Helmut Jarausch <jarau...@skyne t.bewrote:

Hi,

I need to hash arrays of integers (from the hash module).

So, I have to derive from array and supply a __hash__ method.

I don't believe you need to derive from an array.

Here are two simple and well known hash functions you can use readily:

def djbhash(a):
"""Hash function from D J Bernstein"""

h = 5381L
for i in a:
t = (h * 33) & 0xffffffffL
h = t ^ i

return h
def fnvhash(a):
"""Fowler, Noll, Vo Hash function"""
h = 2166136261
for i in a:
t = (h * 16777619) & 0xffffffffL
h = t ^ i

return h

if __name__ == '__main__':
arr = [1001, 3001, 5001, 9001, 10011, 10013, 10015, 10017, 10019,
20011, 23001]
print djbhash(arr)
print fnvhash(arr)
And finally, here is an excellent page that explains hash functions:
http://eternallyconfuzzled.com/tuts/...t_hashing.aspx

Here is Noll's page where he explains the FNV Hash:
http://www.isthe.com/chongo/tech/comp/fnv/

Hope this helps,
--
Sudhi