Opened 8 years ago
Closed 8 years ago
#6672 closed defect (fixed)
[with patch, positive review] Elliptic curve isogeny coercion of output to codomain curve takes too long
Reported by: | shumow | Owned by: | shumow |
---|---|---|---|
Priority: | minor | Milestone: | sage-4.1.2 |
Component: | elliptic curves | Keywords: | |
Cc: | shumow@… | Merged in: | Sage 4.1.2.alpha0 |
Authors: | William Stein, Dan Shumow, John Cremona | Reviewers: | John Cremona, Alex Ghitza |
Report Upstream: | Work issues: | ||
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
As per William's debugging, the correct behavior is to coerce the tuple with check=False.
On Mon, Aug 3, 2009 at 6:10 PM, VictorMiller?<victorsmiller@…> wrote:
Sorry, here's the definition of Q:
Q = E.random_element()
Victor
On Aug 3, 8:45 pm, Simon King <simon.k...@…> wrote:
Hi!
On 4 Aug., 02:31, VictorMiller? <victorsmil...@…> wrote:
Here are the commands I used:
qq = [z for z in primes(100000,100000+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(100000,100000+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, best of 3: 71.2 µs per loop 625 loops, best of 3: 69.3 µs per loop 625 loops, best of 3: 70.8 µs per loop 625 loops, best of 3: 69.2 µs per loop 625 loops, best of 3: 70.2 µs per loop 625 loops, best of 3: 70.7 µs per loop 625 loops, best of 3: 70 µs per loop 625 loops, best of 3: 71 µs per loop 625 loops, best of 3: 70 µs per loop 625 loops, best of 3: 70.2 µs per loop 625 loops, best of 3: 70.1 µs per loop 625 loops, best of 3: 70 µs per loop 625 loops, best of 3: 70.1 µs per loop 625 loops, best of 3: 70.1 µs per loop
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 hope the above is helpful and that somebody opens a trac ticket and submits a patch. I have to get back to what I was doing... I also hope the above email provides some ideas as to how to quickly get to the bottom of questions like this. Note that I did all this in < 10 minutes by using ?? to see where relevant source code is, putting in some return statements (often better than print statements), and knowing that P(...) means P.call.
-- William
Attachments (3)
Change History (8)
Changed 8 years ago by
comment:1 Changed 8 years ago by
- Summary changed from Elliptic curve isogeny coercion of output to codomain curve takes too long to [with patch, needs review] Elliptic curve isogeny coercion of output to codomain curve takes too long
comment:2 Changed 8 years ago by
- Cc shumow@… added; shumow removed
Changed 8 years ago by
comment:3 Changed 8 years ago by
Trac just lost my long comment, explaining what I did complete with test data and timings. Reviewer can ask me if they want to know.
comment:4 Changed 8 years ago by
- Milestone set to sage-4.1.2
- Reviewers set to John Cremona, Alex Ghitza
- Summary changed from [with patch, needs review] Elliptic curve isogeny coercion of output to codomain curve takes too long to [with patch, positive review] Elliptic curve isogeny coercion of output to codomain curve takes too long
Positive review. Apply the three patches in order.
Tested on some random examples such as:
BEFORE THE PATCHES:
sage: E = EllipticCurve('109a').change_ring(GF(71)) sage: lis = E.rational_points() sage: P = lis[20] sage: timeit('E(P)') 625 loops, best of 3: 840 µs per loop
AFTER THE PATCHES:
sage: E = EllipticCurve('109a').change_ring(GF(71)) sage: lis = E.rational_points() sage: P = lis[20] sage: timeit('E(P)') 625 loops, best of 3: 191 µs per loop
comment:5 Changed 8 years ago by
- Merged in set to Sage 4.1.2.alpha0
- Resolution set to fixed
- Status changed from new to closed
Apply after previous