speed up cached_function and cached_method

[Jason Grout]

There are a number of inefficiencies in the critical path (i.e., the code path when values have already been cached) that are addressed in this patch.

PS: The latest patch does in fact much more: Both the critical and the non-critical path are improved, using various tricks.

[Jason Grout]

BEFORE PATCH:

sage: def g(i=15):
...       return sum(range(2**i))
...
sage: @cached_function
sage: def cached_g(i=15):
...       return sum(range(2**i))
...
sage: class A:
...       @cached_method
...       def decorator_cache(self, i=15):
...           return sum(range(2**i))
...       def fast_cache(self, i=15):
...           try:
...               return self._fast_cache
...           except AttributeError:
...               self._fast_cache=sum(range(2**i))
...               return self._fast_cache
sage: timeit('g()')
125 loops, best of 3: 2.02 ms per loop
sage: timeit('cached_g()')
625 loops, best of 3: 37.9 µs per loop
sage: timeit('cached_g()')
625 loops, best of 3: 41.8 µs per loop
sage: c=A()
sage: timeit('c.decorator_cache()')
625 loops, best of 3: 64.8 µs per loop
sage: timeit('c.fast_cache()')
625 loops, best of 3: 1.06 µs per loop

AFTER PATCH

sage: def g(i=15):
...       return sum(range(2**i))
...
sage: @cached_function
sage: def cached_g(i=15):
...       return sum(range(2**i))
...
sage: class A:
...       @cached_method
...       def decorator_cache(self, i=15):
...           return sum(range(2**i))
...       def fast_cache(self, i=15):
...           try:
...               return self._fast_cache
...           except AttributeError:
...               self._fast_cache=sum(range(2**i))
...               return self._fast_cache
sage: timeit('g()')
125 loops, best of 3: 2.94 ms per loop
sage: timeit('cached_g()')
625 loops, best of 3: 1.64 µs per loop
sage: c=A()
sage: timeit('c.decorator_cache()')
625 loops, best of 3: 22 µs per loop
sage: timeit('c.fast_cache()')
625 loops, best of 3: 678 ns per loop

[Jason Grout]

A few doctests don't pass, including one troubling one that seems to indicate that @cached_method isn't computing the right values in a simple case. In the cases in the timings above, the right values are calculated.

[David Loeffler]

Might it not be better for @cached_method to store its cache as an attribute of the instance object, rather than having a single cache which stores the values for all instances of that class?

E.g. the following code works for methods with no arguments:

def fast_cached_method(func):
    def fast_func(some_instance):
        try:
            return getattr(some_instance, '_cache_' + func.__name__)
        except AttributeError:
            result = func(some_instance)
            foo_instance.__dict__['_cache_' + func.__name__] = result
            return result
    return fast_func

I tested this and it's only about 1.5 times slower than doing the caching "by hand", while your speeded-up version above is still about 40 times slower.

David

[Simon King]

I just noticed that the patch does not apply anymore. I am trying to work on cached_function and cached_method anyway, so, I hope that I can soon submit a new patch.

[Simon King]

Hi Jason,

Note also that your patch would break the cache in the case of default/named arguments. Namely, when you have a function def f(n=3): return n^2 then the values of f(), f(3) and f(n=3) should be identical, but they aren't when you have a special case for f().

The patch that I am now preparing is quite thorough, attacking several spots that created overhead. It can now nearly compete with manual caching. I am currently adding more doctests and hope that I will be able to provide a patch later today.

Best regards,

Simon

[Simon King]

Replying to davidloeffler:

Might it not be better for @cached_method to store its cache as an attribute of the instance object, rather than having a single cache which stores the values for all instances of that class?

It was not the case that there was a single cache for all instances (the cache was in the instance for cached_method resp. in the parent of the instance for cached_in_parent_method). However, a part of the overhead came from the fact that the cached method itself has not been an attribute of the instance but of its class.

I just attached a new patch that goes far beyond Jason's approach.

These examples show how the cached method performance is improved by my patch:

Using instance attributes

Polynomial ideals have a cached method groebner_basis. Without my patch, asking for I.groebner_basis would return a CachedMethodCaller - always a new instance whenever the cached method is requested. Of course, that's a waste of time. Therefore, I store the cached method caller as an attribute of the instance, which is done when the attribute is first requested:

sage: R.<x, y, z> = PolynomialRing(QQ, 3)
sage: I = R*(x^3 + y^3 + z^3,x^4-y^4)
sage: I.__dict__.has_key('groebner_basis')
False
sage: I.groebner_basis
Cached version of <function groebner_basis at 0x15a0668>
sage: I.__dict__['groebner_basis']
Cached version of <function groebner_basis at 0x15a0668>
sage: I.groebner_basis is I.groebner_basis # False without my patch
True

This already yields a considerable speedup. However, pickling posed a problem: Since the cached method caller is in the instance's dictionary, it would be attempted to pickle it when the instance is pickled. But functions can not be pickled.

The solution is "creative" (I hope you don't find it crazy - at least it works!):

• CachedMethodCaller has a __reduce__ method, that creates a pickle - but when unpickling it, something else is created, namely an instance of the new class CachedMethodPickle. It only knows the name of the original cached method, and it knows the instance to which it belongs.

• Now, after unpickling, one wants to work with the cached method. Working means: Requesting attributes (like __call__). CachedMethodPickle has a __getattr__ method, which first removes the entry of the instance's dictionary pointing to it; so, it effectively commits suicide.

• Since the CachedMethodPickle has been removed, the original cached method is again available from the class of the instance.

Here is an example:

sage: I.groebner_basis()
[y^5*z^3 - 1/4*x^2*z^6 + 1/2*x*y*z^6 + 1/4*y^2*z^6, x^2*y*z^3 - x*y^2*z^3 + 2*y^3*z^3 + z^6, x*y^3 + y^4 + x*z^3, x^3 + y^3 + z^3]

We now pickle and unpickle the ideal. The cached method groebner_basis is replaced by a placeholder::

sage: J = loads(dumps(I))
sage: J.groebner_basis
Pickle of the cached method "groebner_basis"

But as soon as any other attribute is requested from the placeholder, it replaces itself by the cached method, and the entries of the cache are actually preserved::

sage: J.groebner_basis.is_in_cache()
True
sage: J.groebner_basis
Cached version of <function groebner_basis at 0x...>
sage: J.groebner_basis() == I.groebner_basis()
True

Creating the cache key

1. I found that most of the overhead comes from the computation

of the cache key. It relies on sage.misc.function_mangling.ArgumentFixer. Internally, it works on lists and has some loops. So, I thought it would benefit from Cython - and indeed it does!

Moreover, I made a shortpath in the method fix_to_pos: If there are no named arguments then the result is essentially the list of positional arguments plus the list of arguments with default value.

2. Some more cache key improvements take place inside sage.misc.cachefunc.

Originally, the key was obtained by a method get_key, which was then calling _get_instance_key. In order to reduce the overhead of calling two methods, I directly inserted the code of _get_instance_key and removed that method.

3. I also use Jason's idea of creating a shortpath for the common case

of an empty argument list. However, if the argument list is empty, there might still be arguments with a default value. But we want that explicitly providing these default values yields the same cache key - hence, the following would not work with Jason's patch (continuing the example above):

sage: I.groebner_basis(algorithm='') is I.groebner_basis()
True

The solution is to compute the cache key for an empty argument list once, and store the result for later. That's another reason why it is good to have one CachedMethodCaller permanently attached to an instance (rather than always creating a new one), since otherwise caching of the default key would be difficult.

Accessing the cache

Originally, a method get_cache was used to get the cache dictionary. In some cases, that method used to call another one, _get_instance_cache. Hence, again, there was an overhead of calling two methods.

By my patch, the cache is always available as an attribute of the CachedMethodCaller instance - hence, access is superfast. There is almost no memory problem, since it is simply a new pointer to a dictionary that is an attribute of the instance (resp. of its parent):

sage: I.groebner_basis.cache is I._cache__groebner_basis
True

There is an additional benefit of this approach: If the instance has no __dict__ and does not accept an attribute to be set, it is still possible to cache the method. Similarly, if the parent of the instance does not accept attributes to be set, cached_in_parent_method would still result in a cached method (but it would be cached in the instance, not in its parent).

Documentation

I extended the documentation - but I did not cover ClearCacheOnPickle, which my patch does not change. Apart from that, the doctest coverage of sage.misc.cachefunc is complete. For sage.misc.function_mangling, the coverage script complains "Please add a TestSuite(s).run() doctest." I don't know were that comes from.

Of course, all doctests pass for me. I did not test whether the documentation looks nice in html.

Performance

Last but not least, what the ticket is about: Performance!

Here is the setting:

sage: class Foo:
....:     def __init__(self,P=None):
....:         if P is None:
....:             self._parent=self
....:         else:
....:             self._parent=P
....:     @cached_method
....:     def bar(self,m,n=3):
....:         return m^n
....:     @cached_in_parent_method
....:     def barP(self,m,n=3):
....:         return m^n
....:     def parent(self):
....:         return self._parent
....:
sage: F = Foo()
sage: F_ZZ = Foo(ZZ)

Without my patch

# cache in F:
sage: F.bar(2,3) is F.bar(2) is F.bar(2,n=3) is F.bar(n=3,m=2)
True
sage: timeit('F.bar(2)', number=10000)
10000 loops, best of 3: 18 µs per loop
sage: timeit('F.bar(2,3)', number=10000)
10000 loops, best of 3: 18.2 µs per loop
sage: timeit('F.bar(2,n=3)', number=10000)
10000 loops, best of 3: 20.2 µs per loop
sage: timeit('F.bar(n=3,m=2)', number=10000)
10000 loops, best of 3: 20.2 µs per loop

# cache in F as a parent of itself:
sage: F.barP(2,3) is F.barP(2)  # BUG!
False
sage: F.barP.get_key(2,3)
((<__main__.Foo instance at 0x4570d88>, 2, 3), ())
sage: F.barP.get_key(2)
((<__main__.Foo instance at 0x4570d88>, 2), ())
sage: timeit('F.barP(2)', number=10000)
10000 loops, best of 3: 21.9 µs per loop
sage: timeit('F.barP(2,3)', number=10000)
10000 loops, best of 3: 22.4 µs per loop
sage: timeit('F.barP(2,n=3)', number=10000)
10000 loops, best of 3: 23.8 µs per loop
sage: timeit('F.barP(n=3,m=2)', number=10000)
10000 loops, best of 3: 24.5 µs per loop

# cache in ZZ, which does not allow attribute assignment
sage: F_ZZ.barP(2)
Traceback (most recent call last):
...
AttributeError: 'dictproxy' object has no attribute 'setdefault'

With my patch

# cache in F:
sage: F.bar(2,3) is F.bar(2) is F.bar(2,n=3) is F.bar(n=3,m=2)
True
sage: timeit('F.bar(2)', number=10000)
10000 loops, best of 3: 3.27 µs per loop
sage: timeit('F.bar(2,3)', number=10000)
10000 loops, best of 3: 3.26 µs per loop
sage: timeit('F.bar(2,n=3)', number=10000)
10000 loops, best of 3: 3.63 µs per loop
sage: timeit('F.bar(n=3,m=2)', number=10000)
10000 loops, best of 3: 3.69 µs per loop

# cache in F as parent of itself:
# The bug has disappeared
sage: F.barP(2,3) is F.barP(2) is F.barP(2,n=3) is F.barP(n=3,m=2)
True
sage: timeit('F.barP(2)', number=10000)
10000 loops, best of 3: 6.09 µs per loop
sage: timeit('F.barP(2,3)', number=10000)
10000 loops, best of 3: 5.5 µs per loop
sage: timeit('F.barP(2,n=3)', number=10000)
10000 loops, best of 3: 5.86 µs per loop
sage: timeit('F.barP(n=3,m=2)', number=10000)
10000 loops, best of 3: 6.03 µs per loop

# cache in ZZ, which does not allow attribute assignment.
# It works, since the cache is now automatically moved
# to F_ZZ, as a last resort
sage: F_ZZ.barP(2,3) is F_ZZ.barP(2) is F_ZZ.barP(2,n=3) is F_ZZ.barP(n=3,m=2)
True
sage: timeit('F_ZZ.barP(2)', number=10000)
10000 loops, best of 3: 5.6 µs per loop
sage: timeit('F_ZZ.barP(2,3)', number=10000)
10000 loops, best of 3: 5.56 µs per loop
sage: timeit('F_ZZ.barP(2,n=3)', number=10000)
10000 loops, best of 3: 5.86 µs per loop
sage: timeit('F_ZZ.barP(n=3,m=3)', number=10000)
10000 loops, best of 3: 6.1 µs per loop

Here is the effect of using a shortpath:

sage: class BAR:
....:     @cached_method
....:     def bar(self,m=2,n=3):
....:         return m^n
....:
sage: B = BAR()
sage: B.bar() is B.bar(2,3)
True

Without my patch:

sage: timeit('B.bar(n=2,m=3)', number=10000)
10000 loops, best of 3: 20.4 µs per loop
sage: timeit('B.bar()', number=10000)
10000 loops, best of 3: 17.1 µs per loop

With my patch:

sage: timeit('B.bar(n=2,m=3)', number=10000)
10000 loops, best of 3: 3.73 µs per loop
sage: timeit('B.bar()', number=10000)
10000 loops, best of 3: 1.95 µs per loop

[Simon King]

For the patchbot:

Apply trac8611_cached_method_overhaul.patch

[Simon King]

I forgot to provide a comparison against an explicitly coded cache:

sage: class Foo:
....:     @cached_method
....:     def decorator_bar(self, n=15):
....:         return sum(range(2**n))
....:     def manual_bar(self, n=15):
....:         try:
....:             D = self._my_cache
....:         except AttributeError:
....:             D = self._my_cache = {}
....:             D[n] = sum(range(2**n))
....:         return D[n]
....:
sage: F = Foo()
sage: F.decorator_bar() is F.decorator_bar()
True
sage: F.decorator_bar() == F.manual_bar()
True
sage: F.manual_bar() is F.manual_bar()
True
sage: timeit('F.manual_bar()', number=10000)
10000 loops, best of 3: 1.02 µs per loop
sage: timeit('F.decorator_bar()', number=10000)
10000 loops, best of 3: 1.71 µs per loop
sage: timeit('F.decorator_bar(15)', number=10000)
10000 loops, best of 3: 3.05 µs per loop

Hence, the new version of cached methods can almost compete with an explicitly coded cache, but is of course much more comfortable for the programmer.

[Simon King]

I forgot to mention another bug fix (that is also doctested). It is about the comparison of representations of symmetric groups:

sage: spc = SymmetricGroupRepresentation([3])
sage: spc.important_info = 'Sage rules'
sage: spc == SymmetricGroupRepresentation([3]) # this used to return False!
True

The ticket description states that the improvements concern the critical path (i.e., the value is already caught). Here is one more comparison, that also shows what happens in the non-critical path.

Setting:

sage: class A:
....:     @cached_method
....:     def bar(self,x):
....:         return x
....:     @cached_in_parent_method
....:     def barP(self,x):
....:         return x
....:     def parent(self):
....:         return self
....:     
sage: a = A()

Without my patch:

# The non-critical path:
sage: time for x in range(10^6): b=a.bar(x)
CPU times: user 24.97 s, sys: 0.16 s, total: 25.13 s
Wall time: 25.13 s
sage: time for x in range(10^6): b=a.barP(x)
CPU times: user 41.03 s, sys: 0.13 s, total: 41.16 s
Wall time: 41.17 s

# The critical path (now the values are cached):
sage: time for x in range(10^6): b=a.bar(x)
CPU times: user 16.45 s, sys: 0.02 s, total: 16.47 s
Wall time: 16.47 s
sage: time for x in range(10^6): b=a.barP(x)
CPU times: user 20.47 s, sys: 0.02 s, total: 20.50 s
Wall time: 20.50 s

With my patch:

# The non-critical path:
sage: time for x in range(10^6): b=a.bar(x)
CPU times: user 11.40 s, sys: 0.08 s, total: 11.48 s
Wall time: 11.48 s
sage: time for x in range(10^6): b=a.barP(x)
CPU times: user 27.89 s, sys: 0.12 s, total: 28.01 s
Wall time: 28.02 s

# The critical path (now the values are cached):
sage: time for x in range(10^6): b=a.bar(x)
CPU times: user 3.09 s, sys: 0.01 s, total: 3.10 s
Wall time: 3.10 s
sage: time for x in range(10^6): b=a.barP(x)
CPU times: user 5.25 s, sys: 0.02 s, total: 5.26 s
Wall time: 5.26 s

Hence, the patch improves all cases.

[Simon King]

In the patch version that I've just attached, I also inserted the documentation of sage.misc.cachedfunc and (after cleaning the documentation) of sage.misc.function_mangling into the reference manual. I think the documentation looks nice, but perhaps the referee can have a look on it as well.

[Simon King]

Improved performance for cached methods; add documentation to reference manual; cache is_subcateory. Replaces Jason's patch

[Simon King]

I slightly changed the patch. But the small change has in fact a big impact:

The method sage.categories.category.Category.is_subcategory is used to test whether something is an object of a given category. Due to the omnipresence of categories in Sage, this test occurs very often. So, it should be optimised!

I suggest that is_subcategory should be cached. I.e., the new patch version differs from the old one only in the line "@cached_method" in front of that method.

I believe that the additional memory consumption is affordable: When starting Sage, there are precisely 55 categories, so, in the worst case, caching is_subcategory adds 55 cache dictionaries with 55 entries.

The impact on the overall performance is obvious: On my machine, sage -tp 4 sage takes 1721.2 seconds without my patch, but 1643.8 seconds with my patch.

Hence, the average improvement is about 4.5%.

[David Loeffler]

Apply trac8611_cached_method_overhaul.patch

(for the patchbot)

[Simon King]

Replying to davidloeffler:

Apply trac8611_cached_method_overhaul.patch

(for the patchbot)

There already was such message for the patchbot.

But one question: On sage-devel, Robert Bradshaw reported that I need to rebase the patch. But the patchbot - at least in one attempt - succeeded. So, what is the status?

Unfortunately, I seriously screwed up my Sage installations. Currently, my two ol installations are broken, and sadly I was unablee to build either sage-4.6.1 or sage-4.6.2.alpha0/1.

Cheers,

Simon

[David Loeffler]

Replying to SimonKing:

Replying to davidloeffler:

Apply trac8611_cached_method_overhaul.patch

(for the patchbot)

There already was such message for the patchbot.

Patchbot's a bit pedantic about formatting of such messages. If you look at the records of the test runs it's done, you'll see that prior to today it was trying to apply both patches at once, and thus failing, and after I prodded it earlier, it did a new run which passed.

I've got a working 4.6.2.alpha0 build, so I can test it against that tomorrow morning.

[David Loeffler]

Applies fine and passes doctests both using 4.6.2.alpha0 on my system, and using 4.6.1 with patchbot. I ran some tests and in the case of a method with no arguments it's something like 15 times faster than the old code and only a tiny bit slower than a hand-rolled cache. Code looks fine by eye, and it's great that you added these modules to the ref manual as well. Positive review.

I'm looking forward to using %prun in future sage versions and not finding that 20% of the execution time has been spent in "fix_to_pos", which is frequently the case at the moment...

[Jeroen Demeyer]

Please use line breaks in the commit message if it is so long. Make sure the first line is a short description of the patch with the ticket number. Following lines can contain a longer description.

[David Loeffler]

Apply only this patch

[David Loeffler]

Done.

[Simon King]

Replying to davidloeffler:

Done.

Thank you!

[Nicolas M. Thiéry]

For the record, a related thread:

• ​http://groups.google.com/group/sage-devel/browse_thread/thread/6607a3919c619345