% Related Modules
%    PersistentMapping
%    PersistentList
%    BTrees
%       Total Ordering and Persistence
%       BTree Diagnostic Tools

\section{Related Modules}

The ZODB package includes a number of related modules that provide
useful data types such as BTrees.

\subsection{\module{persistent.mapping.PersistentMapping}}

The \class{PersistentMapping} class is a wrapper for mapping objects
that will set the dirty bit when the mapping is modified by setting or
deleting a key.

\begin{funcdesc}{PersistentMapping}{container = \{\}}
Create a \class{PersistentMapping} object that wraps the
mapping object \var{container}.  If you don't specify a
value for \var{container}, a regular Python dictionary is used.
\end{funcdesc}

\class{PersistentMapping} objects support all the same methods as
Python dictionaries do.

\subsection{\module{persistent.list.PersistentList}}

The \class{PersistentList} class is a wrapper for mutable sequence objects,
much as \class{PersistentMapping} is a wrapper for mappings.

\begin{funcdesc}{PersistentList}{initlist = []}
Create a \class{PersistentList} object that wraps the
mutable sequence object \var{initlist}.  If you don't specify a
value for \var{initlist}, a regular Python list is used.
\end{funcdesc}

\class{PersistentList} objects support all the same methods as
Python lists do.


\subsection{BTrees Package}

When programming with the ZODB, Python dictionaries aren't always what
you need.  The most important case is where you want to store a very
large mapping.  When a Python dictionary is accessed in a ZODB, the
whole dictionary has to be unpickled and brought into memory.  If
you're storing something very large, such as a 100,000-entry user
database, unpickling such a large object will be slow.  BTrees are a
balanced tree data structure that behave like a mapping but distribute
keys throughout a number of tree nodes.  The nodes are stored in
sorted order (this has important consequences -- see below).  Nodes are
then only unpickled and brought into memory as they're accessed, so the
entire tree doesn't have to occupy memory (unless you really are
touching every single key).

The BTrees package provides a large collection of related data
structures.  There are variants of the data structures specialized to
integers, which are faster and use less memory.  There
are four modules that handle the different variants.  The first two
letters of the module name specify the types of the keys and values in
mappings -- O for any object and I for integer.  For example, the
\module{BTrees.IOBTree} module provides a mapping with integer
keys and arbitrary objects as values.

The four data structures provide by each module are a BTree, a Bucket,
a TreeSet, and a Set.  The BTree and Bucket types are mappings and
support all the usual mapping methods, e.g. \function{update()} and
\function{keys()}.  The TreeSet and Set types are similar to mappings
but they have no values; they support the methods that make sense for
a mapping with no keys, e.g. \function{keys()} but not
\function{items()}.  The Bucket and Set types are the individual
building blocks for BTrees and TreeSets, respectively.  A Bucket or
Set can be used when you are sure that it will have few elements.  If
the data structure will grow large, you should use a BTree or TreeSet.
Like Python lists, Buckets and Sets are allocated in one
contiguous piece, and insertions and deletions can take time
proportional to the number of existing elements.  Also like Python lists,
a Bucket or Set is a single object, and is pickled and unpickled in its
entirety.  BTrees and TreeSets are multi-level tree structures with
much better (logarithmic) worst-case time bounds, and the tree structure
is built out of multiple objects, which ZODB can load individually
as needed.

The four modules are named \module{OOBTree}, \module{IOBTree},
\module{OIBTree}, and \module{IIBTree}.  The two letter prefixes are
repeated in the data types names.  The \module{BTrees.OOBTree} module
defines the following types: \class{OOBTree}, \class{OOBucket},
\class{OOSet}, and \class{OOTreeSet}.  Similarly, the other three modules
each define their own variants of those four types.

The \function{keys()}, \function{values()}, and \function{items()}
methods on BTree and TreeSet types do not materialize a list with all
of the data.  Instead, they return lazy sequences that fetch data
from the BTree as needed.  They also support optional arguments to
specify the minimum and maximum values to return, often called "range
searching".  Because all these types are stored in sorted order, range
searching is very efficient.

The \function{keys()}, \function{values()}, and \function{items()}
methods on Bucket and Set types do return lists with all the data.
Starting in ZODB 3.3, there are also \function{iterkeys()},
\function{itervalues()}, and \function{iteritems()} methods that
return iterators (in the Python 2.2 sense).  Those methods also apply to
BTree and TreeSet objects.

A BTree object supports all the methods you would expect of a mapping,
with a few extensions that exploit the fact that the keys are sorted.
The example below demonstrates how some of the methods work.  The
extra methods are \function{minKey()} and \function{maxKey()}, which
find the minimum and maximum key value subject to an optional bound
argument, and \function{byValue()}, which should probably be ignored
(it's hard to explain exactly what it does, and as a result it's
almost never used -- best to consider it deprecated).  The various
methods for enumerating keys, values and items also accept minimum
and maximum key arguments ("range search"), and (new in ZODB 3.3)
optional Boolean arguments to control whether a range search is
inclusive or exclusive of the range's endpoints.

\begin{verbatim}
>>> from BTrees.OOBTree import OOBTree
>>> t = OOBTree()
>>> t.update({1: "red", 2: "green", 3: "blue", 4: "spades"})
>>> len(t)
4
>>> t[2]
'green'
>>> s = t.keys() # this is a "lazy" sequence object
>>> s
<OOBTreeItems object at 0x0088AD20>
>>> len(s)  # it acts like a Python list
4
>>> s[-2]
3
>>> list(s) # materialize the full list
[1, 2, 3, 4]
>>> list(t.values())
['red', 'green', 'blue', 'spades']
>>> list(t.values(1, 2)) # values at keys in 1 to 2 inclusive
['red', 'green']
>>> list(t.values(2))    # values at keys >= 2
['green', 'blue', 'spades']
>>> list(t.values(min=1, max=4))  # keyword args new in ZODB 3.3
['red', 'green', 'blue', 'spades']
>>> list(t.values(min=1, max=4, excludemin=True, excludemax=True))
['green', 'blue']
>>> t.minKey()     # smallest key
1
>>> t.minKey(1.5)  # smallest key >= 1.5
2
>>> for k in t.keys():
...     print k,
1 2 3 4
>>> for k in t:    # new in ZODB 3.3
...     print k,
1 2 3 4
>>> for pair in t.iteritems():  # new in ZODB 3.3
...     print pair,
...
(1, 'red') (2, 'green') (3, 'blue') (4, 'spades')
>>> t.has_key(4)  # returns a true value, but exactly what undefined
2
>>> t.has_key(5)
0
>>> 4 in t  # new in ZODB 3.3
True
>>> 5 in t  # new in ZODB 3.3
False
>>>

\end{verbatim}

% XXX I'm not sure all of the following is actually correct.  The
% XXX set functions have complicated behavior.
Each of the modules also defines some functions that operate on
BTrees -- \function{difference()}, \function{union()}, and
\function{intersection()}.  The \function{difference()} function returns
a Bucket, while the other two methods return a Set.
If the keys are integers, then the module also defines
\function{multiunion()}.  If the values are integers, then the module
also defines \function{weightedIntersection()} and
\function{weightedUnion()}.  The function doc strings describe each
function briefly.

\code{BTrees/Interfaces.py} defines the operations, and is the official
documentation.  Note that the interfaces don't define the concrete types
returned by most operations, and you shouldn't rely on the concrete types
that happen to be returned:  stick to operations guaranteed by the
interface.  In particular, note that the interfaces don't specify anything
about comparison behavior, and so nothing about it is guaranteed.  In ZODB
3.3, for example, two BTrees happen to use Python's default object
comparison, which amounts to comparing the (arbitrary but fixed) memory
addresses of the BTrees. This may or may not be true in future releases.
If the interfaces don't specify a behavior, then whether that behavior
appears to work, and exactly happens if it does appear to work, are
undefined and should not be relied on.

\subsubsection{Total Ordering and Persistence}

The BTree-based data structures differ from Python dicts in several
fundamental ways.  One of the most important is that while dicts
require that keys support hash codes and equality comparison,
the BTree-based structures don't use hash codes and require a total
ordering on keys.

Total ordering means three things:

\begin{enumerate}
\item  Reflexive.  For each \var{x}, \code{\var{x} == \var{x}} is true.

\item  Trichotomy.  For each \var{x} and \var{y}, exactly one of
       \code{\var{x} < \var{y}}, \code{\var{x} == \var{y}}, and
       \code{\var{x} > \var{y}} is true.

\item  Transitivity.  Whenever \code{\var{x} <= \var{y}} and
       \code{\var{y} <= \var{z}}, it's also true that
       \code{\var{x} <= \var{z}}.
\end{enumerate}

The default comparison functions for most objects that come with Python
satisfy these rules, with some crucial cautions explained later.  Complex
numbers are an example of an object whose default comparison function
does not satisfy these rules:  complex numbers only support \code{==}
and \code{!=} comparisons, and raise an exception if you try to compare
them in any other way.  They don't satisfy the trichotomy rule, and must
not be used as keys in BTree-based data structures (although note that
complex numbers can be used as keys in Python dicts, which do not require
a total ordering).

Examples of objects that are wholly safe to use as keys in BTree-based
structures include ints, longs, floats, 8-bit strings, Unicode strings,
and tuples composed (possibly recursively) of objects of wholly safe
types.

It's important to realize that even if two types satisfy the
rules on their own, mixing objects of those types may not.  For example,
8-bit strings and Unicode strings both supply total orderings, but mixing
the two loses trichotomy; e.g., \code{'x' < chr(255)} and
\code{u'x' == 'x'}, but trying to compare \code{chr(255)} to
\code{u'x'} raises an exception.  Partly for this reason (another is
given later), it can be dangerous to use keys with multiple types in
a single BTree-based structure.  Don't try to do that, and you don't
have to worry about it.

Another potential problem is mutability:  when a key is inserted in a
BTree-based structure, it must retain the same order relative to the
other keys over time.  This is easy to run afoul of if you use mutable
objects as keys.  For example, lists supply a total ordering, and then

\begin{verbatim}
>>> L1, L2, L3 = [1], [2], [3]
>>> from BTrees.OOBTree import OOSet
>>> s = OOSet((L2, L3, L1))  # this is fine, so far
>>> list(s.keys())           # note that the lists are in sorted order
[[1], [2], [3]]
>>> s.has_key([3])           # and [3] is in the set
1
>>> L2[0] = 5                # horrible -- the set is insane now
>>> s.has_key([3])           # for example, it's insane this way
0
>>> s
OOSet([[1], [5], [3]])
>>>
\end{verbatim}

Key lookup relies on that the keys remain in sorted order (an efficient
form of binary search is used).  By mutating key L2 after inserting it,
we destroyed the invariant that the OOSet is sorted.  As a result, all
future operations on this set are unpredictable.

A subtler variant of this problem arises due to persistence:  by default,
Python does several kinds of comparison by comparing the memory
addresses of two objects.  Because Python never moves an object in memory,
this does supply a usable (albeit arbitrary) total ordering across the
life of a program run (an object's memory address doesn't change).  But
if objects compared in this way are used as keys of a BTree-based
structure that's stored in a database, when the objects are loaded from
the database again they will almost certainly wind up at different
memory addresses.  There's no guarantee then that if key K1 had a memory
address smaller than the memory address of key K2 at the time K1 and
K2 were inserted in a BTree, K1's address will also be smaller than
K2's when that BTree is loaded from a database later.  The result will
be an insane BTree, where various operations do and don't work as
expected, seemingly at random.

Now each of the types identified above as "wholly safe to use" never
compares two instances of that type by memory address, so there's
nothing to worry about here if you use keys of those types.  The most
common mistake is to use keys that are instances of a user-defined class
that doesn't supply its own \method{__cmp__()} method.  Python compares
such instances by memory address.  This is fine if such instances are
used as keys in temporary BTree-based structures used only in a single
program run.  It can be disastrous if that BTree-based structure is
stored to a database, though.

\begin{verbatim}
>>> class C:
...     pass
...
>>> a, b = C(), C()
>>> print a < b   # this may print 0 if you try it
1
>>> del a, b
>>> a, b = C(), C()
>>> print a < b   # and this may print 0 or 1
0
>>>
\end{verbatim}

That example illustrates that comparison of instances of classes that
don't define \method{__cmp__()} yields arbitrary results (but consistent
results within a single program run).

Another problem occurs with instances of classes that do define
\method{__cmp__()}, but define it incorrectly.  It's possible but
rare for a custom \method{__cmp__()} implementation to violate one
of the three required formal properties directly.  It's more common for
it to "fall back" to address-based comparison by mistake.
For example,

\begin{verbatim}
class Mine:
    def __cmp__(self, other):
        if other.__class__ is Mine:
            return cmp(self.data, other.data)
        else:
            return cmp(self.data, other)
\end{verbatim}

It's quite possible there that the \keyword{else} clause allows
a result to be computed based on memory address.  The bug won't show
up until a BTree-based structure uses objects of class \class{Mine} as
keys, and also objects of other types as keys, and the structure is
loaded from a database, and a sequence of comparisons happens to execute
the \keyword{else} clause in a case where the relative order of object
memory addresses happened to change.

This is as difficult to track down as it sounds, so best to stay far
away from the possibility.

You'll stay out of trouble by follwing these rules, violating them
only with great care:

\begin{enumerate}
\item  Use objects of simple immutable types as keys in
       BTree-based data structures.

\item  Within a single BTree-based data structure, use objects of
       a single type as keys.  Don't use multiple key types in a
       single structure.

\item  If you want to use class instances as keys, and there's
       any possibility that the structure may be stored in a
       database, it's crucial that the class define a
       \method{__cmp__()} method, and that the method is
       carefully implemented.

       Any part of a comparison implementation that relies (explicitly
       or implicitly) on an address-based comparison result will
       eventually cause serious failure.
\end{enumerate}


\subsubsection{BTree Diagnostic Tools}

A BTree (or TreeSet) is a complex data structure, really a graph of
variable-size nodes, connected in multiple ways via three distinct kinds
of C pointers.  There are some tools available to help check internal
consistency of a BTree as a whole.

Most generally useful is the \module{BTrees.check} module.  The
\function{check.check()} function examines a BTree (or Bucket, Set, or
TreeSet) for value-based consistency, such as that the keys are in
strictly increasing order.  See the function docstring for details.
The \function{check.display()} function displays the internal structure
of a BTree.

BTrees and TreeSets also have a \method{_check()} method.  This verifies
that the (possibly many) internal pointers in a BTree or TreeSet
are mutually consistent, and raises \exception{AssertionError} if they're
not.

If a \function{check.check()} or \method{_check()} call fails,
it may point to a bug in the implementation of BTrees or conflict
resolution, or may point to database corruption.

Repairing a damaged BTree is usually best done by making a copy of it.
For example, if \var{self.data} is bound to a corrupted IOBTree,

\begin{verbatim}
    self.data = IOBTree(self.data)
\end{verbatim}

usually suffices.  If object identity needs to be preserved,

\begin{verbatim}
    acopy = IOBTree(self.data)
    self.data.clear()
    self.data.update(acopy)
\end{verbatim}

does the same, but leaves \var{self.data} bound to the same object.
