# hashing an array - howto

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### Helmut Jarausch

Sep 5, 2008, 10:38:41 AM9/5/08
to
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

Sep 5, 2008, 10:57:12 AM9/5/08
to
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.tostring())

Peter

### bearoph...@lycos.com

Sep 5, 2008, 11:18:52 AM9/5/08
to
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(somelist, tuple)
hash(tuple(somelist))

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

Sep 5, 2008, 11:49:28 AM9/5/08
to
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.

### bearoph...@lycos.com

Sep 5, 2008, 12:45:37 PM9/5/08
to
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

### John Machin

Sep 5, 2008, 4:58:00 PM9/5/08
to
On Sep 6, 2:45 am, bearophileH...@lycos.com wrote:
> 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:

Perhaps the OP shouldn't be constructing the hash of a mutable object.
Perhaps he would be grateful if his hash function raised an exception

>
> >>> 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))

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

Perhaps the OP (who hasn't stated what he is going to use the hash
results for) needs to use only the values in his hash, and would be if
not highly delighted then at least blithely unconcerned if it turned
out that [1, 2, 3] and (1, 2, 3) had the same hash.

>
> 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.
>

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

Your alternative solution using reduce and xor may have suboptimal
characteristics ... xor_hash((1, 2, 3)) == xor_hash((1, 3, 2)) ==
xor_hash((2, 1, 3)) etc. While the docs for __hash__ say "it is
advised to somehow mix together (e.g., using exclusive or) the hash
values for the components of the object", in practice "somehow" is
rather more elaborate than xor. Have a look at the tuplehash function
in .../Objects/tupleobject.c. If the order of the values in the tuple
doesn't matter, then perhaps the OP really should be using a set (or a
bag).

Cheers,
John

### bearoph...@lycos.com

Sep 5, 2008, 5:49:21 PM9/5/08
to
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

Sep 5, 2008, 7:30:35 PM9/5/08
to
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

Sep 5, 2008, 7:55:27 PM9/5/08
to

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 ...

### Robert Kern

Sep 8, 2008, 4:53:02 PM9/8/08
to pytho...@python.org
bearoph...@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?

Because that's the kind of hash that dicts expect. If two objects are equal
(i.e. (x==y) is True), they need to have their hash values equal as well. In
order to do a lookup into a dict, it will hash the key and search the table for
a that hash value. If there are multiple keys with the same hash value, then the
dict will compare the keys by value to find a match. Since (123==123.0==123L),
they must also have the same hash value such that

{123.0: 'got it'}[123] == 'got it'

--
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
that is made terrible by our own mad attempt to interpret it as though it had
an underlying truth."
-- Umberto Eco

### sudhi...@gmail.com

Sep 12, 2008, 2:05:56 AM9/12/08
to
On Sep 5, 9:38 am, Helmut Jarausch <jarau...@skynet.be> wrote:
> 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/algorithms/jsw_tut_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