#6059: [with patch; needs review] speed regresion in hilbert_symbol after #5834
---------------------------+------------------------------------------------
Reporter: tornaria | Owner: tornaria
Type: defect | Status: new
Priority: major | Milestone: sage-4.0
Component: number theory | Keywords: regression
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Comment(by tornaria):
I screwed it up the first version, because I was trying to avoid overhead.
The original code, good for integers only (before #5834) was:
{{{
a = ZZ(a)
}}}
My first version was
{{{
a = ZZ(a.numerator() * a.denominator())
}}}
which breaks when {{{a}}} is a (python) {{{int}}}. The new version is
{{{
a = QQ(a).numerator() * QQ(a).denominator()
}}}
which should be safe for all purposes (my first version was in between).
Indeed, I'm a bit concerned about overhead. Compare the trivial
{{{
sage: timeit("hilbert_symbol(1,1,-1)")
625 loops, best of 3: 10.3 µs per loop
}}}
using the original code (only good for integers) vs.
{{{
sage: timeit("hilbert_symbol(1,1,-1)")
625 loops, best of 3: 19.1 µs per loop
}}}
with the new code (good for rationals).
And check out the speed of the actual computation:
{{{
sage: a = ZZ.random_element(10^50)
sage: b = ZZ.random_element(10^50)
sage: p = next_prime(ZZ.random_element(10^50))
sage: timeit("pari(a).hilbert(b,p)")
625 loops, best of 3: 3.13 µs per loop
}}}
Is there a standard/suggested way of writing the preamble of a function
(where parameters are checked, coerced, etc) to minimize overhead in a
fast path?
(I guess this is what one buys with a dynamic language... and moving this
to cython could help if really necessary).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6059#comment:2>
Sage <http://sagemath.org/>
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