On Nov 30, 2006, at 10:54 PM, William Stein wrote:

>> You need to try this last one again in pyrex, using a cdef int i for
>> the loop counter, and doing the arithmetic with python ints; and then
>> compare that to the same thing using SAGE Integers.
>
> OK, I've done that.  But honestly, I don't know what it is really  
> timing,
> since the optimizing compiler could be doing all kinds of interesting
> things with unrolling loops, macros, etc.  And it's really pretty  
> unfair,
> since the point is optimizing an interpreter rather than a compiler.
> With that benchmark though, object creation is basically 12 times  
> faster
> for Python ints, though again I think one has to be careful in  
> intepreting
> how these things mean, when we're really trying to benchmark an  
> interpreter
> and the object-creation-overhead of that interpreter.

I agree that the interpreter setting is important. But the compiled  
setting is important too. For example, if you write a pyrex function  
that operates on matrices, whose elements are arbitrary python  
objects, and you happen to give it a matrix with python ints as  
entries, it will go something like 12 times faster than if you had  
given it a matrix with SAGE ints. Well, not 12, but still probably  
significant.

David


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