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Union slowdown when SameTest is specified

  • To: mathgroup at smc.vnet.net
  • Subject: [mg101378] Union slowdown when SameTest is specified
  • From: J Siehler <jsiehler at gmail.com>
  • Date: Fri, 3 Jul 2009 05:40:19 -0400 (EDT)
Hello group!  I was a little surprised and puzzled by the following:

In[1]:= $Version
Out[1]= "7.0 for Mac OS X PowerPC (32-bit) (November 10, 2008)"

In[2]:= data = RandomInteger[{1, 10}, {5000, 2, 12}];
Timing[Union[data];]
Out[3]= {0.008138, Null}

So far so good; so far so speedy.  But why does this happen:

In[4]:= Timing[Union[data, SameTest -> Equal];]
Out[4]= {15.313, Null}

Or more egregiously,

In[5]:= Timing[Union[data, SameTest -> (First@#1 == First@#2 &)];]
Out[5]= {86.293, Null}

There's nothing special about the form of the data here, just it
happens to be similar in form to the data I was working on when I
experienced terrible slowdown with the SameTest that I've shown in the
third example - which doesn't seem like a demanding comparison.    So
can anyone explain the orders-of-magnitude change in times here?  Much
appreciated!
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