# Containers for storing coercion data¶

This module provides TripleDict and MonoDict. These are structures similar to WeakKeyDictionary in Python’s weakref module, and are optimized for lookup speed. The keys for TripleDict consist of triples (k1,k2,k3) and are looked up by identity rather than equality. The keys are stored by weakrefs if possible. If any one of the components k1, k2, k3 gets garbage collected, then the entry is removed from the TripleDict.

Key components that do not allow for weakrefs are stored via a normal refcounted reference. That means that any entry stored using a triple (k1,k2,k3) so that none of the k1,k2,k3 allows a weak reference behaves as an entry in a normal dictionary: Its existence in TripleDict prevents it from being garbage collected.

That container currently is used to store coercion and conversion maps between two parents (trac ticket #715) and to store homsets of pairs of objects of a category (trac ticket #11521). In both cases, it is essential that the parent structures remain garbage collectable, it is essential that the data access is faster than with a usual WeakKeyDictionary, and we enforce the “unique parent condition” in Sage (parent structures should be identical if they are equal).

MonoDict behaves similarly, but it takes a single item as a key. It is used for caching the parents which allow a coercion map into a fixed other parent (trac ticket #12313).

By trac ticket #14159, MonoDict and TripleDict can be optionally used with weak references on the values.

Note that this kind of dictionary is also used for caching actions and coerce maps. In previous versions of Sage, the cache was by strong references and resulted in a memory leak in the following example. However, this leak was fixed by trac ticket #715, using weak references:

sage: K.<t> = GF(2^55)
sage: for i in range(50):
....:     a = K.random_element()
....:     E = EllipticCurve(j=a)
....:     P = E.random_point()
....:     Q = 2*P
sage: L = [Partitions(n) for n in range(200)]  # purge strong cache in CachedRepresentation
sage: import gc
sage: n = gc.collect()
sage: from sage.schemes.elliptic_curves.ell_finite_field import EllipticCurve_finite_field
sage: LE = [x for x in gc.get_objects() if isinstance(x, EllipticCurve_finite_field)]
sage: len(LE)
1

class sage.structure.coerce_dict.MonoDict

Bases: object

This is a hashtable specifically designed for (read) speed in the coercion model.

It differs from a python WeakKeyDictionary in the following important ways:

• Comparison is done using the ‘is’ rather than ‘==’ operator.
• Only weak references to the keys are stored if at all possible. Keys that do not allow for weak references are stored with a normal refcounted reference.
• The callback of the weak references is safe against recursion, see below.

There are special cdef set/get methods for faster access. It is bare-bones in the sense that not all dictionary methods are implemented.

IMPLEMENTATION:

It is implemented as a hash table with open addressing, similar to python’s dict.

INPUT:

• data – optional iterable defining initial data, as dict or iterable of (key, value) pairs.
• weak_values – optional bool (default False). If it is true, weak references to the values in this dictionary will be used, when possible.

EXAMPLES:

sage: from sage.structure.coerce_dict import MonoDict
sage: L = MonoDict()
sage: a = 'a'; b = 'ab'; c = '-15'
sage: L[a] = 1
sage: L[b] = 2
sage: L[c] = 3


The key is expected to be a unique object. Hence, the item stored for c can not be obtained by providing another equal string:

sage: L[a]
1
sage: L[b]
2
sage: L[c]
3
sage: L['-15']
Traceback (most recent call last):
...
KeyError: '-15'


Not all features of Python dictionaries are available, but iteration over the dictionary items is possible:

sage: sorted(L.items())
[('-15', 3), ('a', 1), ('ab', 2)]
sage: del L[c]
sage: sorted(L.items())
[('a', 1), ('ab', 2)]
sage: len(L)
2
sage: for i in range(1000):
....:     L[i] = i
sage: len(L)
1002
sage: L['a']
1
sage: L['c']
Traceback (most recent call last):
...
KeyError: 'c'


Note that MW also accepts values that do not allow for weak references:

    sage: MW[k] = int(5)
sage: MW[k]
5

The following demonstrates that :class:MonoDict is safer than
:class:~weakref.WeakKeyDictionary against recursions created by nested
callbacks; compare :trac:15069 (the mechanism used now is different, though)::

sage: M = MonoDict()
sage: class A: pass
sage: a = A()
sage: prev = a
sage: for i in range(1000):
....:     newA = A()
....:     M[prev] = newA
....:     prev = newA
sage: len(M)
1000
sage: del a
sage: len(M)
0

The corresponding example with a Python :class:weakref.WeakKeyDictionary
would result in a too deep recursion during deletion of the dictionary
items::

sage: import weakref
sage: M = weakref.WeakKeyDictionary()
sage: a = A()
sage: prev = a
sage: for i in range(1000):
....:     newA = A()
....:     M[prev] = newA
....:     prev = newA
sage: len(M)
1000
sage: del a  # py2 -- does not appear to be an issue on Python 3
Exception RuntimeError: 'maximum recursion depth exceeded...' in <function remove at ...> ignored
sage: len(M) > 0  # py2
True

Check that also in the presence of circular references, :class:MonoDict
gets properly collected::

sage: import gc
sage: def count_type(T):
....:     return len([c for c in gc.get_objects() if isinstance(c,T)])
sage: _ = gc.collect()
sage: N = count_type(MonoDict)
sage: for i in range(100):
....:     V = [MonoDict({"id":j+100*i}) for j in range(100)]
....:     n= len(V)
....:     for i in range(n): V[i][V[(i+1)%n]]=(i+1)%n
....:     del V
....:     _ = gc.collect()
....:     assert count_type(MonoDict) == N
sage: count_type(MonoDict) == N
True

AUTHORS:

- Simon King (2012-01)
- Nils Bruin (2012-08)
- Simon King (2013-02)
- Nils Bruin (2013-11)

copy()

Return a copy of this MonoDict as Python dict.

EXAMPLES:

sage: from sage.structure.coerce_dict import MonoDict
sage: L = MonoDict()
sage: L[1] = 42
sage: L.copy()
{1: 42}

items()

Iterate over the (key, value) pairs of this MonoDict.

EXAMPLES:

sage: from sage.structure.coerce_dict import MonoDict
sage: L = MonoDict()
sage: L[1] = None
sage: L[2] = True
sage: L.items()
<generator object at ...>
sage: sorted(L.items())
[(1, None), (2, True)]

class sage.structure.coerce_dict.MonoDictEraser

Bases: object

Erase items from a MonoDict when a weak reference becomes invalid.

This is of internal use only. Instances of this class will be passed as a callback function when creating a weak reference.

EXAMPLES:

sage: from sage.structure.coerce_dict import MonoDict
sage: class A: pass
sage: a = A()
sage: M = MonoDict()
sage: M[a] = 1
sage: len(M)
1
sage: del a
sage: import gc
sage: n = gc.collect()
sage: len(M)    # indirect doctest
0


AUTHOR:

• Simon King (2012-01)
• Nils Bruin (2013-11)
class sage.structure.coerce_dict.ObjectWrapper

Bases: object

A simple fast wrapper around a Python object. This is like a 1-element tuple except that it does not keep a reference to the wrapped object.

class sage.structure.coerce_dict.TripleDict

Bases: object

This is a hashtable specifically designed for (read) speed in the coercion model.

It differs from a python dict in the following important ways:

• All keys must be sequence of exactly three elements. All sequence types (tuple, list, etc.) map to the same item.
• Any of the three key components that support weak-refs are stored via a weakref. If any of these components gets garbage collected then the entire entry is removed. In that sense, this structure behaves like a nested WeakKeyDictionary.
• Comparison is done using the ‘is’ rather than ‘==’ operator.

There are special cdef set/get methods for faster access. It is bare-bones in the sense that not all dictionary methods are implemented.

INPUT:

• data – optional iterable defining initial data, as dict or iterable of (key, value) pairs.
• weak_values – optional bool (default False). If it is true, weak references to the values in this dictionary will be used, when possible.

IMPLEMENTATION:

It is implemented as a hash table with open addressing, similar to python’s dict.

EXAMPLES:

sage: from sage.structure.coerce_dict import TripleDict
sage: L = TripleDict()
sage: a = 'a'; b = 'b'; c = 'c'
sage: L[a,b,c] = 1
sage: L[a,b,c]
1
sage: L[c,b,a] = -1
sage: sorted(L.items())
[(('a', 'b', 'c'), 1), (('c', 'b', 'a'), -1)]
sage: del L[a,b,c]
sage: list(L.items())
[(('c', 'b', 'a'), -1)]
sage: len(L)
1
sage: for i in range(1000):
....:     L[i,i,i] = i
sage: len(L)
1001
sage: L = TripleDict(L)
sage: L[c,b,a]
-1
sage: L[a,b,c]
Traceback (most recent call last):
...
KeyError: ('a', 'b', 'c')
sage: L[a]
Traceback (most recent call last):
...
KeyError: 'a'
sage: L[a] = 1
Traceback (most recent call last):
...
KeyError: 'a'


AUTHORS:

• Simon King, 2012-01
• Nils Bruin, 2012-08
• Simon King, 2013-02
• Nils Bruin, 2013-11
copy()

Return a copy of this TripleDict as Python dict.

EXAMPLES:

sage: from sage.structure.coerce_dict import TripleDict
sage: L = TripleDict()
sage: L[1,2,3] = 42
sage: L.copy()
{(1, 2, 3): 42}

items()

Iterate over the (key, value) pairs of this TripleDict.

EXAMPLES:

sage: from sage.structure.coerce_dict import TripleDict
sage: L = TripleDict()
sage: L[1,2,3] = None
sage: L.items()
<generator object at ...>
sage: list(L.items())
[((1, 2, 3), None)]

class sage.structure.coerce_dict.TripleDictEraser

Bases: object

Erases items from a TripleDict when a weak reference becomes invalid.

This is of internal use only. Instances of this class will be passed as a callback function when creating a weak reference.

EXAMPLES:

sage: from sage.structure.coerce_dict import TripleDict
sage: class A: pass
sage: a = A()
sage: T = TripleDict()
sage: T[a,ZZ,None] = 1
sage: T[ZZ,a,1] = 2
sage: T[a,a,ZZ] = 3
sage: len(T)
3
sage: del a
sage: import gc
sage: n = gc.collect()
sage: len(T) # indirect doctest
0


AUTHOR:

• Simon King (2012-01)
• Nils Bruin (2013-11)