Steven D'Aprano wrote:

> On Mon, 22 Mar 2010 22:05:40 -0700, Paul Rubin wrote:
> 
>> Antoine Pitrou <solip...@pitrou.net> writes:
>>> "Orders of magnitude worse", in any case, sounds very exaggerated.
>> 
>> The worst case can lose orders of magnitude if a lot of values hash to
>> the same bucket.
> 
> 
> Well, perhaps one order of magnitude.
> 
> 
>>>> for i in xrange(100):
> ...     n = 32*i+1
> ...     assert hash(2**n) == hash(2)
> ...
>>>> d1 = dict.fromkeys(xrange(100))
>>>> d2 = dict.fromkeys([2**(32*i+1) for i in xrange(100)])
>>>>
>>>> from timeit import Timer
>>>> setup = "from __main__ import d1, d2"
>>>> t1 = Timer("for k in d1.keys(): x = d1[k]", setup)
>>>> t2 = Timer("for k in d2.keys(): x = d2[k]", setup)
>>>>
>>>> min(t1.repeat(number=1000, repeat=5))
> 0.026707887649536133
>>>> min(t2.repeat(number=1000, repeat=5))
> 0.33103203773498535

But the ratio grows with the number of collisions:

$ python extrapolate.py            
10                                 
0.00120401382446                   
0.00753307342529                   
ratio: 6.25663366337               

100
0.00542402267456
0.316139936447  
ratio: 58.2851428571

1000
0.00553417205811
3.36690688133
ratio: 608.384930209

$ cat extrapolate.py
from timeit import Timer

class Item(object):
    def __init__(self, value, hash=None):
        self.value = value
        self.hash = value if hash is None else hash
    def __eq__(self, other):
        return self.value == other.value
    def __hash__(self):
        return self.hash

setup = "from __main__ import d"
bench = "for k in d: x = d[k]"

for n, number in (10,100), (100,100), (1000,10):
    print n
    d1 = dict.fromkeys(Item(i) for i in xrange(n))
    d2 = dict.fromkeys(Item(i, 0) for i in xrange(n))
    ab = []
    for d in d1, d2:
        t = Timer(bench, setup)
        ab.append(min(t.repeat(number=number, repeat=3)))
        print ab[-1]
    print "ratio:", ab[1]/ab[0]
    print


See also http://xkcd.com/605/

Peter
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