Log function and documentation revamp

[rws]

From ​https://groups.google.com/forum/?hl=en#!topic/sage-devel/hwm-7V8S3hE

sage: log(int(8),2)
log(8)/log(2)
sage: log(8,int(2))
log(8)/log(2)
sage: log(8,2)
3

Also:
sage: log(1/8,2)
log(1/8)/log(2)

sage: ((-1)^(-I*log(3)/pi)).n()
3.00000000000000
sage: log(3,-1)
...
ValueError: m must be positive

[rws]

New commits:

​0086ec0

18970: always simplify log(a^m,a) if possible

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​92d9762

18970: fix

[dkrenn]

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).

[dkrenn]

sage: log(QQ(8),2).parent()
Integer Ring

which is a different behavior compared to the common/similar arithmetic operations (e.g. (QQ(2)^ZZ(1)).parent() is Rational Field and not Integer Ring) and I would expect that the logarithm of a rational is again a rational (if possible) or something where QQ coerces into (but not out of something which coerces into QQ).

[rws]

Is this a one-time comment, or do you plan to review to the end?

[dkrenn]

Replying to rws:

Is this a one-time comment, or do you plan to review to the end?

Does this make a difference on how to react to my comment? ;) ....or more seriously: I am not sure if I feel qualified enough to review a change in the log-function. I just saw the discussion on sage-devel and looked into the ticket and decided to give some comments.

[rws]

The code at hand unconditionally tries to coerce the arguments into ZZ,QQ instead of checking the type first. Apart from the speed issue it also would benefit from moving completely into GiNaC: atm some cases are intercepted unnecessarily in Function_log.__call__ which itself awkwardly calls Pynac.

[leif]

I guess some of the speed regression is due to the at least partially redundant checking whether arg == base**v, and of course now in addition computing the valuation first in case the latter does not hold. (At least it seemed to when I looked at it yesterday...)

Not sure how much the probably superfluous coercion contributes.

[rws]

New branch depends on Pynac git master.

---

New commits:

​11a81ee

18970: add two-arg log()

[rws]

Timings with this branch. Before:

sage: %timeit log(QQ(8),2)
The slowest run took 10.96 times longer than the fastest. This could mean that an intermediate result is being cached.
10000 loops, best of 3: 40.1 µs per loop
sage: %timeit log(QQ(8),2)
10000 loops, best of 3: 40.2 µs per loop
sage: %timeit log(QQ(8),3)
10000 loops, best of 3: 40.5 µs per loop
sage: %timeit log(ZZ(8),3)
10000 loops, best of 3: 34.4 µs per loop
sage: %timeit log(ZZ(8),2)
The slowest run took 19.11 times longer than the fastest. This could mean that an intermediate result is being cached.
1000000 loops, best of 3: 886 ns per loop

After:

sage: %timeit log(QQ(8),2)
The slowest run took 15.53 times longer than the fastest. This could mean that an intermediate result is being cached.
10000 loops, best of 3: 26.7 µs per loop
sage: %timeit log(QQ(8),3)
The slowest run took 10.80 times longer than the fastest. This could mean that an intermediate result is being cached.
10000 loops, best of 3: 26.8 µs per loop
sage: %timeit log(ZZ(8),3)
10000 loops, best of 3: 30.2 µs per loop
sage: %timeit log(ZZ(8),2)
The slowest run took 17.37 times longer than the fastest. This could mean that an intermediate result is being cached.
1000000 loops, best of 3: 686 ns per loop

The single run measurements vary so much from run to run that I refrain from giving them here. The After values of timeit('log(QQ(8),3)', number=1, repeat=1) are however in the same range as the Before values (as well as the others).

[rws]

New commits:

​02427f6

redo log function

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​584c4f3	Merge branch 'develop' into t/18970/log_function_bugs_with_int_and_negative_base
​456cc14	18970: doc restructuring to get the most out of typing log?

[rws]

Completed coverage.

---

New commits:

​838c1fd

18970: Log function and documentation revamp

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​3c34001

Merge branch 'develop' into t/18970/18970-2

[chapoton]

does not apply

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​94cc4a5	Merge branch 'develop' into t/18970/18970-2
​e46bc47	18970: fix and robustify doctests

[tscrim]

Needs another rebase over beta9.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​7ab331e

Merge branch 'develop' into t/18970/18970-2

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​b3b9a52

18970: fix log usage

[rws]

Fixes were added, cruft removed, and it all squashed.

---

New commits:

​b0486c8

18970: Log function and documentation revamp

[tscrim]

LGTM. Timings on my laptop with branch:

sage: %timeit log(QQ(8),2)
The slowest run took 29.31 times longer than the fastest. This could mean that an intermediate result is being cached.
1000000 loops, best of 3: 1.57 µs per loop
sage: %timeit log(QQ(8),3)
The slowest run took 4.03 times longer than the fastest. This could mean that an intermediate result is being cached.
10000 loops, best of 3: 35.5 µs per loop
sage: %timeit log(ZZ(8),3)
10000 loops, best of 3: 33 µs per loop
sage: %timeit log(ZZ(8),2)
The slowest run took 16.93 times longer than the fastest. This could mean that an intermediate result is being cached.
1000000 loops, best of 3: 887 ns per loop

vs. with develop:

sage: %timeit log(QQ(8),2)
The slowest run took 14987.26 times longer than the fastest. This could mean that an intermediate result is being cached.
1000000 loops, best of 3: 1.6 µs per loop
sage: %timeit log(QQ(8),3)
10000 loops, best of 3: 43.2 µs per loop
sage: %timeit log(ZZ(8),3)
The slowest run took 4.42 times longer than the fastest. This could mean that an intermediate result is being cached.
10000 loops, best of 3: 38.9 µs per loop
sage: %timeit log(ZZ(8),2)
The slowest run took 14.23 times longer than the fastest. This could mean that an intermediate result is being cached.
1000000 loops, best of 3: 1.06 µs per loop

[rws]

Thanks.