#18970: always simplify log(a^m,a) to m for any a,m coercible to Integer
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Reporter: rws | Owner:
Type: defect | Status: needs_info
Priority: major | Milestone: sage-6.9
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: Ralf Stephan | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/rws/always_simplify_log_a_m_a__to_m_for_any_a_m_coercible_to_integer|
92d9762ad28880ef81a4781a0eee34b50accc1c6
Dependencies: | Stopgaps:
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Changes (by dkrenn):
* status: needs_review => needs_info
Comment:
Before this patch
{{{
sage: %timeit log(QQ(8),2)
The slowest run took 5.08 times longer than the fastest. This could mean
that an intermediate result is being cached
10000 loops, best of 3: 39.4 µs per loop
sage: %timeit log(QQ(8),3)
10000 loops, best of 3: 38.1 µs per loop
sage: %timeit log(ZZ(8),3)
10000 loops, best of 3: 32.8 µs per loop
sage: %timeit log(ZZ(8),2)
The slowest run took 14.52 times longer than the fastest. This could mean
that an intermediate result is being cached
1000000 loops, best of 3: 1.12 µs per loop
}}}
After
{{{
sage: %timeit log(QQ(8),3)
The slowest run took 37.28 times longer than the fastest. This could mean
that an intermediate result is being cached
10000 loops, best of 3: 48.8 µs per loop
sage: %timeit log(QQ(8),2)
The slowest run took 8.69 times longer than the fastest. This could mean
that an intermediate result is being cached
100000 loops, best of 3: 5.43 µs per loop
sage: %timeit log(ZZ(8),3)
10000 loops, best of 3: 48.4 µs per loop
sage: %timeit log(ZZ(8),2)
The slowest run took 8.80 times longer than the fastest. This could mean
that an intermediate result is being cached
100000 loops, best of 3: 5.34 µs per loop
}}}
I've repeated (differently) it due to the caching-warnings. Before
{{{
sage: timeit('log(QQ(8),3)', number=1, repeat=1)
1 loops, best of 1: 191 µs per loop
sage: timeit('log(QQ(8),2)', number=1, repeat=1)
1 loops, best of 1: 150 µs per loop
sage: timeit('log(ZZ(8),3)', number=1, repeat=1)
1 loops, best of 1: 125 µs per loop
sage: timeit('log(ZZ(8),2)', number=1, repeat=1)
1 loops, best of 1: 24.1 µs per loop
}}}
After
{{{
sage: timeit('log(QQ(8),3)', number=1, repeat=1)
1 loops, best of 1: 1.93 ms per loop
sage: timeit('log(QQ(8),2)', number=1, repeat=1)
1 loops, best of 1: 45.1 µs per loop
sage: timeit('log(ZZ(8),3)', number=1, repeat=1)
1 loops, best of 1: 158 µs per loop
sage: timeit('log(ZZ(8),2)', number=1, repeat=1)
1 loops, best of 1: 45.1 µs per loop
}}}
In particular `log(QQ(8),3)` becomes much slower (and only `log(QQ(8),2)`
gains speed).
--
Ticket URL: <http://trac.sagemath.org/ticket/18970#comment:6>
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