On 10 Sep, 07:18, Robert Bradshaw <[email protected]>
wrote:
> On Sep 9, 2009, at 10:38 PM, Bill Hart wrote:
>
> > This program only takes 0.68s in C using a pretty naive mpz program on
> > sage.math. I doubt the memory allocation is really relevant. The
> > interpreter overhead is by far the greatest component
>
> Not allocation of the mpz_t's themselves, but allocation of the
> wrapping objects (or, even if there's a pool, the recycling of them).
> Maybe you count this in interpreter overhead.
Thanks, that occurred to me afterwards. So, I think you are right. If
there are no mpz's or adds the time drops dramatically.
sage: def fibo(n):
a=1
b=1
c=0
for i in range(n):
c=a
a=b
b=c
return b
...:
sage: def test(n,m):
...: for i in range(m):
...: _=fibo(n)
...:
sage: timeit("test(4000,4000)")
5 loops, best of 3: 1.25 s per loop
With additions but no mpz's
sage: def fibo(n):
a=1
b=1
c=0
for i in range(n):
c=a
a=a+b
c=b
return b
...:
sage: def test(n,m):
...: for i in range(m):
...: _=fibo(n)
...:
sage: timeit("test(4000,4000)")
5 loops, best of 3: 2.66 s per loop
Bill.
>
> There's also coercion overhead--a+b must verify a and b are both
> integers before calling the integer add function. (I'd guess that's
> less than 10-20%.)
>
> - Robert
>
>
>
>
>
> > On 9 Sep, 17:57, Nils Bruin <[email protected]> wrote:
> >> Inspired by a little experiment we did to see if there is room to
> >> improve to ECL's bignum performance, we ran a little experiment
> >> computing fibonacci numbers (we wanted to test addition because it
> >> was
> >> mainly ECL's memory management that was under consideration)
>
> >> with the following defs:
>
> >> def fibo(n):
> >> a=1
> >> b=1
> >> c=0
> >> for i in range(n):
> >> c=a
> >> a=a+b
> >> b=c
> >> return b
>
> >> def test(n,m):
> >> for i in range(m):
> >> _=fibo(n)
>
> >> sage: timeit("test(4000,4000)")
> >> 5 loops, best of 3: 6.99 s per loop
> >> sage: time test(4000,4000)
> >> CPU times: user 7.10 s, sys: 0.00 s, total: 7.10 s
> >> Wall time: 7.11 s
> >> sage: time test(4000,4000)
> >> CPU times: user 7.24 s, sys: 0.00 s, total: 7.24 s
> >> Wall time: 7.24 s
> >> sage: time test(4000,4000)
> >> CPU times: user 7.38 s, sys: 0.00 s, total: 7.38 s
> >> Wall time: 7.39 s
> >> sage: time test(4000,4000)
> >> CPU times: user 7.10 s, sys: 0.00 s, total: 7.10 s
> >> Wall time: 7.11 s
> >> sage: time test(4000,4000)
> >> CPU times: user 7.05 s, sys: 0.00 s, total: 7.05 s
> >> Wall time: 7.06 s
>
> >> In ECL, this took 14.8 sec (uncompiled) and 8.8 sec (compiled). Of
> >> course, this particular programming exercise was just to see how fast
> >> one can shove information into GMP and ECL at this point definitely
> >> doesn't claim to be particularly optimized for that particular task,
> >> but as you can see, straightforward python and sage do a good job.
>
> >> For comparison, Magma takes about 8.4 secs, as does the code above
> >> when I initialize a=int(1) etc.
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