>> Also, does it matter (in term of speed)
>> that SAGE is running on a 64-bit OS vs 32-bit?
>This is not an easy question to answer. Sage is built from many
> components that were not specifically designed with Sage or
> multiprocessor issues in mind.
This is a subtle question indeed. The question, "does it matter in
terms of speed that Sage is running on a 64-bit OS vs 32-bit" is easy
to answer. It *does* matter. But _how_ it matters is very subtle.
Here's an example of Sage running in 64-bit versus 32-bit Linux on
exactly the same hardware (Xeon 2.6Ghz):
64-bit
sage: timeit('factorial(10^6)')
5 loops, best of 3: 1.69 s per loop
32-bit:
sage: timeit('factorial(10^6)')
5 loops, best of 3: 2.04 s per loop
In the above example GMP is able to take advantage of 64-bit to
do the integer arithmetic more quickly.
Here's another example:
64-bit:
sage: time a = random_matrix(ZZ,200).determinant()
CPU times: user 2.74 s, sys: 0.01 s, total: 2.75 s
32-bit:
sage: time a = random_matrix(ZZ,200).determinant()
CPU times: user 0.74 s, sys: 0.04 s, total: 0.78 s
Here, surprisingly, 64-bit is WAY SLOWER than 32-bit at doing the
exact same thing. I don't really understand this. The moral should I
think be that 32 versus 64 bit can be really subtle when it comes to
performance. But as Justin said, one huge plus with 64-bit is that
if you have > 2GB of RAM, you can use it all in one process, but with
32-bit you can't (which sucks).
-- William
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