#3309: massively optimize the binomial function when an input is real or complex
floating point
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Reporter: was | Owner: somebody
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.4.2
Component: basic arithmetic | Keywords:
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Comment(by ddrake):
I'm attaching a patch which uses gamma() when appropriate. We can use this
until we get the fast Pari stuff in. Here are some timings:
{{{
BEFORE
sage: x, y = 1140000.78, 420000
sage: %timeit binomial(x, y)
10 loops, best of 3: 1.03 s per loop
sage: x, y = RR(pi^5), 10
sage: %timeit binomial(x, y)
10000 loops, best of 3: 28.8 µs per loop
sage: x, y = RR(pi^15), 500
sage: %timeit binomial(x, y)
1000 loops, best of 3: 864 µs per loop
sage: x, y = RealField(500)(1729000*sqrt(2)), 17000
sage: %timeit binomial(x, y)
10 loops, best of 3: 35.8 ms per loop
}}}
With the patch:
{{{
AFTER
sage: x, y = 1140000.78, 420000
sage: %timeit binomial(x, y)
1000 loops, best of 3: 302 µs per loop
sage: x, y = RR(pi^5), 10
sage: %timeit binomial(x, y)
10000 loops, best of 3: 188 µs per loop
sage: x, y = RR(pi^15), 500
sage: %timeit binomial(x, y)
1000 loops, best of 3: 362 µs per loop
sage: x, y = RealField(500)(1729000*sqrt(2)), 17000
sage: %timeit binomial(x, y)
1000 loops, best of 3: 743 µs per loop
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3309#comment:3>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
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