speed up construction of kernel polynomial for Vélu isogeny using product tree #40948
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| for xQ in self.__kernel_mod_sign.keys(): | ||
| psi *= x - invX(xQ) | ||
| from sage.misc.misc_c import prod | ||
| psi = prod([x - invX(xQ) for xQ in self.__kernel_mod_sign.keys()]) # building the list is not redundant; this is slightly faster |
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really? prod delegates to iterator_prod if the input is a generator. Where does the overhead come from?
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actually the overhead might be because Python can inline the list comprehension, but not the generator expression.
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doesnt prod use a binary tree for the product when given a list?
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Last time I checked, the difference was that passing an iterator makes it use a different (suboptimal) tree structure since the total length is not a priori known.
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Looking at it again, I'm not sure if that is the reason: iterator_prod() does promise that the tree will be balanced... So you might be right, @user202729.
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Documentation preview for this PR (built with commit c9545c8; changes) is ready! 🎉 |
Nice suggestion. Should we add the |
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I had a look (albeit quickly) for the function in NTL and couldn't see it. So maybe it's just flint that supports it? I dunno what's best. Maybe just a generic python implementation and then a call to library specific functions if they exist. This feels like a good place to introduce the patch but also it could be in a new PR to avoid this taking up more of your time. |
sagemathgh-40948: speed up construction of kernel polynomial for Vélu isogeny using product tree Computing a product of a collection of linear polynomials is best done using a balanced product tree. Example: ```sage sage: E = EllipticCurve(GF(16411), [1,0]) sage: P = E.lift_x(25) sage: phi = E.isogeny(P) sage: assert phi._EllipticCurveIsogeny__algorithm == 'velu' sage: %time _ = phi.kernel_polynomial() ``` Current `develop`: ``` CPU times: user 25.6 ms, sys: 0 ns, total: 25.6 ms Wall time: 25.7 ms ``` This branch: ``` CPU times: user 13.7 ms, sys: 0 ns, total: 13.7 ms Wall time: 13.8 ms ``` URL: sagemath#40948 Reported by: Lorenz Panny Reviewer(s): Giacomo Pope, Lorenz Panny, user202729
sagemathgh-40948: speed up construction of kernel polynomial for Vélu isogeny using product tree Computing a product of a collection of linear polynomials is best done using a balanced product tree. Example: ```sage sage: E = EllipticCurve(GF(16411), [1,0]) sage: P = E.lift_x(25) sage: phi = E.isogeny(P) sage: assert phi._EllipticCurveIsogeny__algorithm == 'velu' sage: %time _ = phi.kernel_polynomial() ``` Current `develop`: ``` CPU times: user 25.6 ms, sys: 0 ns, total: 25.6 ms Wall time: 25.7 ms ``` This branch: ``` CPU times: user 13.7 ms, sys: 0 ns, total: 13.7 ms Wall time: 13.8 ms ``` URL: sagemath#40948 Reported by: Lorenz Panny Reviewer(s): Giacomo Pope, Lorenz Panny, user202729
Computing a product of a collection of linear polynomials is best done using a balanced product tree.
Example:
Current
develop:This branch: