#6199: Integer * int is slow
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Reporter: fredrik.johansson | Owner: somebody
Type: defect | Status: needs_info
Priority: major | Milestone: sage-duplicate/invalid/wontfix
Component: basic arithmetic | Resolution:
Keywords: | Author:
Upstream: N/A | Reviewer:
Merged: | Work_issues:
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Changes (by robertwb):
* status: new => needs_info
Comment:
If we're going to special case, we could override {{{__mul__}}} for
Integer directly, rather than stick stuff in {{{Element.__mul__}}}. That's
"breaking the rules" even more though. Alternatively, we could add a
{{{cdef Element _mul_long(self, long n)}}} method which is checked for
right after the parents aren't the same. This is a bit hackish, but would
provide a good avenue for improvements for other types as well (QQ, RDF).
Do we need addition as well? (No, I don't think this should be extended to
other operands...)
Note that
{{{
sage: timeit("a", number=10**6)
1000000 loops, best of 3: 58.1 ns per loop
}}}
so I wrote my own
{{{
def time_mul(a, b, long n):
cdef long i
for i in range(n):
a*b
}}}
With this, I did a special _mul_long method.
Before:
{{{
sage: a = 123 ; b = 456 ; c = 456r ; y = RDF(pi)
sage: a*c, a*y
(56088, 386.415896392)
sage: %time time_mul(a,b, 10**7)
CPU times: user 1.13 s, sys: 0.00 s, total: 1.13 s
Wall time: 1.13 s
sage: %time time_mul(a,c, 10**7)
CPU times: user 17.14 s, sys: 0.04 s, total: 17.18 s
Wall time: 17.25 s
sage: %time time_mul(a,y, 10**7)
CPU times: user 8.21 s, sys: 0.02 s, total: 8.24 s
Wall time: 8.25 s
}}}
After:
{{{
sage: a = 123 ; b = 456 ; c = 456r ; y = RDF(pi)
sage: a*c, a*y
(56088, 386.415896392)
sage: %time time_mul(a,b, 10**7)
CPU times: user 1.16 s, sys: 0.00 s, total: 1.16 s
Wall time: 1.17 s
sage: %time time_mul(a,c, 10**7)
CPU times: user 0.95 s, sys: 0.00 s, total: 0.96 s
Wall time: 0.96 s
sage: %time time_mul(a,y, 10**7)
CPU times: user 8.52 s, sys: 0.02 s, total: 8.54 s
Wall time: 8.57 s
}}}
I'm leaning towards it being worth it, on the right only, for * and +
only. The cost is (on my machine) an extra 25ns per non-identical-parents
operation, which are at the cheapest is at least 100s of ns.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6199#comment:6>
Sage <http://www.sagemath.org>
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