The above change is very sensible, since we know that outP is on
self.__E2, so should directly create a point on E2 and not check again
that our point is really on E2 (which is very expensive).
I agree that we should make the change:
else:
outP = self.__E2(outP)
to
else:
outP = self.__E2.point(outP,check=False)
When I originally wrote the code I did not know that this problem
existed. I just wanted to map a pair of elements on a field to the
elliptic curve point object associated to those coordinates.
I created the ticket:
http://trac.sagemath.org/sage_trac/ticket/6672
and will fix this when I get home tonight (I'm at work right now.)
The fix is very easy, if someone else wants to grab it for now, that
is fine. But just be sure to set check = false in the other point
coercion call as well (in the if block associated with this else
block.)
Thanks,
Dan
On Mon, Aug 3, 2009 at 7:00 PM, William Steinwst...@gmail.com wrote:
On Mon, Aug 3, 2009 at 6:10 PM, VictorMillervictorsmil...@gmail.com wrote:
Sorry, here's the definition of Q:
Q = E.random_element()
Victor
On Aug 3, 8:45 pm, Simon King simon.k...@nuigalway.ie wrote:
Hi!
On 4 Aug., 02:31, VictorMiller victorsmil...@gmail.com wrote:
Here are the commands I used:
qq = [z for z in primes(10,10+100) if (z%12) == 11]
E = EllipticCurve(j=GF(qq[0])(1728))
# E has qq[0]+1 points over GF(qq[0])
factor(qq[0]+1)
P = ((qq[0]+1)//3)*E.random_element()
K = [E(0),P,-P]
phi = E.isogeny(K)
There appears to be a memory leak -- or some sort of caching (!) -- in
the code to evaluate phi. This is likely impacting the complexity of
the some code that is run during the computation of phi(P). The log
below shows that memory usage increases upon evaluation of phi(P):
sage: get_memory_usage()
210.109375
sage: timeit('phi(P)')
125 loops, best of 3: 7.13 ms per loop
sage: get_memory_usage()
210.609375
sage: timeit('phi(P)')
125 loops, best of 3: 7.3 ms per loop
sage: get_memory_usage()
211.109375
sage: timeit('phi(P)')
125 loops, best of 3: 7.49 ms per loop
sage: get_memory_usage()
211.609375
sage: timeit('phi(P)')
125 loops, best of 3: 7.69 ms per loop
sage: get_memory_usage()
212.109375
Now I looked at the source code for the function phi(P) =
phi.__call__(P) and bisected by putting early returns in. If you
change
else:
outP = self.__E2(outP)
to
else:
return outP
outP = self.__E2(outP)
in that function in ell_curve_isogeny.py (around line 875), then the
leak and slowdown vanishes.
Thus the real problem is in the trivial line self.__E2(outP),
which by the way takes even in good cases like 10 times as long as the
rest of the whole function put together. Indeed, coercing a point
into a curve is a horrendous disaster (this is the real problem,
forget the isogeny stuff):
sage: get_memory_usage()
195.81640625
sage: timeit('E(P)')
625 loops, best of 3: 4.24 ms per loop
sage: get_memory_usage()
201.31640625
In fact, the function E.point is to blame, evidently:
sage: timeit('E.point(P)')
125 loops, best of 3: 4.13 ms per loop
sage: get_memory_usage()
202.08984375
sage: timeit('E.point(P)')
125 loops, best of 3: 4.4 ms per loop
sage: get_memory_usage()
203.08984375
... but *ONLY* with check=True (the default):
sage: timeit('E.point(P,check=False)')
625 loops, best of 3: 8.26 µs per loop
sage: get_memory_usage()
203.08984375
sage: timeit('E.point(P,check=False)')
625 loops, best of 3: 7.29 µs per loop
sage: get_memory_usage()
203.08984375
I.e., we get a speedup of a factor of nearly 1000 by using
check=False, plus the leak goes away. So in the check -- which
involves arithmetic -- maybe the coercion model is surely being
invoked at some point (I guess), and that is perhaps caching
information, thus memory usage goes up and performance goes down. I
don't know, I'm not looking further.
Going back to your original problem, if I change in ell_curve_isogeny.py
else:
outP = self.__E2(outP)
to
else:
outP = self.__E2.point(outP,check=False)
then we have the following, which is exactly what you would hope for
(things are fast, no slowdown).
sage: qq = [z for z in primes(10,10+100) if (z%12) == 11]
sage: E = EllipticCurve(j=GF(qq[0])(1728))
sage: # E has qq[0]+1 points over GF(qq[0])
sage: factor(qq[0]+1)
2^2 * 3 * 5 * 1667
sage: P = ((qq[0]+1)//3)*E.random_element()
sage: K = [E(0),P,-P]
sage: phi = E.isogeny(K)
sage: get_memory_usage()
190.56640625
sage: timeit('phi(P)')
625 loops, best of 3: 69.8 µs per loop
sage: for i in xrange(20): timeit('phi(P)')
:
625 loops, best of 3: 69.3 µs per loop
625 loops, best of 3: 69.3 µs per loop
625 loops, best of 3: 69.6 µs per loop
625 loops, best of 3: 69.9 µs per loop
625 loops, best of 3: 69.8 µs per loop
625 loops, best of 3: 70 µs per loop
625 loops,
