| """functools.py - Tools for working with functions and callable objects | 
 | """ | 
 | # Python module wrapper for _functools C module | 
 | # to allow utilities written in Python to be added | 
 | # to the functools module. | 
 | # Written by Nick Coghlan <ncoghlan at gmail.com>, | 
 | # Raymond Hettinger <python at rcn.com>, | 
 | # and Ćukasz Langa <lukasz at langa.pl>. | 
 | #   Copyright (C) 2006-2013 Python Software Foundation. | 
 | # See C source code for _functools credits/copyright | 
 |  | 
 | __all__ = ['update_wrapper', 'wraps', 'WRAPPER_ASSIGNMENTS', 'WRAPPER_UPDATES', | 
 |            'total_ordering', 'cmp_to_key', 'lru_cache', 'reduce', 'partial', | 
 |            'singledispatch'] | 
 |  | 
 | try: | 
 |     from _functools import reduce | 
 | except ImportError: | 
 |     pass | 
 | from abc import get_cache_token | 
 | from collections import namedtuple | 
 | from types import MappingProxyType | 
 | from weakref import WeakKeyDictionary | 
 | try: | 
 |     from _thread import RLock | 
 | except: | 
 |     class RLock: | 
 |         'Dummy reentrant lock for builds without threads' | 
 |         def __enter__(self): pass | 
 |         def __exit__(self, exctype, excinst, exctb): pass | 
 |  | 
 |  | 
 | ################################################################################ | 
 | ### update_wrapper() and wraps() decorator | 
 | ################################################################################ | 
 |  | 
 | # update_wrapper() and wraps() are tools to help write | 
 | # wrapper functions that can handle naive introspection | 
 |  | 
 | WRAPPER_ASSIGNMENTS = ('__module__', '__name__', '__qualname__', '__doc__', | 
 |                        '__annotations__') | 
 | WRAPPER_UPDATES = ('__dict__',) | 
 | def update_wrapper(wrapper, | 
 |                    wrapped, | 
 |                    assigned = WRAPPER_ASSIGNMENTS, | 
 |                    updated = WRAPPER_UPDATES): | 
 |     """Update a wrapper function to look like the wrapped function | 
 |  | 
 |        wrapper is the function to be updated | 
 |        wrapped is the original function | 
 |        assigned is a tuple naming the attributes assigned directly | 
 |        from the wrapped function to the wrapper function (defaults to | 
 |        functools.WRAPPER_ASSIGNMENTS) | 
 |        updated is a tuple naming the attributes of the wrapper that | 
 |        are updated with the corresponding attribute from the wrapped | 
 |        function (defaults to functools.WRAPPER_UPDATES) | 
 |     """ | 
 |     for attr in assigned: | 
 |         try: | 
 |             value = getattr(wrapped, attr) | 
 |         except AttributeError: | 
 |             pass | 
 |         else: | 
 |             setattr(wrapper, attr, value) | 
 |     for attr in updated: | 
 |         getattr(wrapper, attr).update(getattr(wrapped, attr, {})) | 
 |     # Issue #17482: set __wrapped__ last so we don't inadvertently copy it | 
 |     # from the wrapped function when updating __dict__ | 
 |     wrapper.__wrapped__ = wrapped | 
 |     # Return the wrapper so this can be used as a decorator via partial() | 
 |     return wrapper | 
 |  | 
 | def wraps(wrapped, | 
 |           assigned = WRAPPER_ASSIGNMENTS, | 
 |           updated = WRAPPER_UPDATES): | 
 |     """Decorator factory to apply update_wrapper() to a wrapper function | 
 |  | 
 |        Returns a decorator that invokes update_wrapper() with the decorated | 
 |        function as the wrapper argument and the arguments to wraps() as the | 
 |        remaining arguments. Default arguments are as for update_wrapper(). | 
 |        This is a convenience function to simplify applying partial() to | 
 |        update_wrapper(). | 
 |     """ | 
 |     return partial(update_wrapper, wrapped=wrapped, | 
 |                    assigned=assigned, updated=updated) | 
 |  | 
 |  | 
 | ################################################################################ | 
 | ### total_ordering class decorator | 
 | ################################################################################ | 
 |  | 
 | def total_ordering(cls): | 
 |     """Class decorator that fills in missing ordering methods""" | 
 |     convert = { | 
 |         '__lt__': [('__gt__', lambda self, other: not (self < other or self == other)), | 
 |                    ('__le__', lambda self, other: self < other or self == other), | 
 |                    ('__ge__', lambda self, other: not self < other)], | 
 |         '__le__': [('__ge__', lambda self, other: not self <= other or self == other), | 
 |                    ('__lt__', lambda self, other: self <= other and not self == other), | 
 |                    ('__gt__', lambda self, other: not self <= other)], | 
 |         '__gt__': [('__lt__', lambda self, other: not (self > other or self == other)), | 
 |                    ('__ge__', lambda self, other: self > other or self == other), | 
 |                    ('__le__', lambda self, other: not self > other)], | 
 |         '__ge__': [('__le__', lambda self, other: (not self >= other) or self == other), | 
 |                    ('__gt__', lambda self, other: self >= other and not self == other), | 
 |                    ('__lt__', lambda self, other: not self >= other)] | 
 |     } | 
 |     # Find user-defined comparisons (not those inherited from object). | 
 |     roots = [op for op in convert if getattr(cls, op, None) is not getattr(object, op, None)] | 
 |     if not roots: | 
 |         raise ValueError('must define at least one ordering operation: < > <= >=') | 
 |     root = max(roots)       # prefer __lt__ to __le__ to __gt__ to __ge__ | 
 |     for opname, opfunc in convert[root]: | 
 |         if opname not in roots: | 
 |             opfunc.__name__ = opname | 
 |             opfunc.__doc__ = getattr(int, opname).__doc__ | 
 |             setattr(cls, opname, opfunc) | 
 |     return cls | 
 |  | 
 |  | 
 | ################################################################################ | 
 | ### cmp_to_key() function converter | 
 | ################################################################################ | 
 |  | 
 | def cmp_to_key(mycmp): | 
 |     """Convert a cmp= function into a key= function""" | 
 |     class K(object): | 
 |         __slots__ = ['obj'] | 
 |         def __init__(self, obj): | 
 |             self.obj = obj | 
 |         def __lt__(self, other): | 
 |             return mycmp(self.obj, other.obj) < 0 | 
 |         def __gt__(self, other): | 
 |             return mycmp(self.obj, other.obj) > 0 | 
 |         def __eq__(self, other): | 
 |             return mycmp(self.obj, other.obj) == 0 | 
 |         def __le__(self, other): | 
 |             return mycmp(self.obj, other.obj) <= 0 | 
 |         def __ge__(self, other): | 
 |             return mycmp(self.obj, other.obj) >= 0 | 
 |         def __ne__(self, other): | 
 |             return mycmp(self.obj, other.obj) != 0 | 
 |         __hash__ = None | 
 |     return K | 
 |  | 
 | try: | 
 |     from _functools import cmp_to_key | 
 | except ImportError: | 
 |     pass | 
 |  | 
 |  | 
 | ################################################################################ | 
 | ### partial() argument application | 
 | ################################################################################ | 
 |  | 
 | def partial(func, *args, **keywords): | 
 |     """new function with partial application of the given arguments | 
 |     and keywords. | 
 |     """ | 
 |     def newfunc(*fargs, **fkeywords): | 
 |         newkeywords = keywords.copy() | 
 |         newkeywords.update(fkeywords) | 
 |         return func(*(args + fargs), **newkeywords) | 
 |     newfunc.func = func | 
 |     newfunc.args = args | 
 |     newfunc.keywords = keywords | 
 |     return newfunc | 
 |  | 
 | try: | 
 |     from _functools import partial | 
 | except ImportError: | 
 |     pass | 
 |  | 
 |  | 
 | ################################################################################ | 
 | ### LRU Cache function decorator | 
 | ################################################################################ | 
 |  | 
 | _CacheInfo = namedtuple("CacheInfo", ["hits", "misses", "maxsize", "currsize"]) | 
 |  | 
 | class _HashedSeq(list): | 
 |     """ This class guarantees that hash() will be called no more than once | 
 |         per element.  This is important because the lru_cache() will hash | 
 |         the key multiple times on a cache miss. | 
 |  | 
 |     """ | 
 |  | 
 |     __slots__ = 'hashvalue' | 
 |  | 
 |     def __init__(self, tup, hash=hash): | 
 |         self[:] = tup | 
 |         self.hashvalue = hash(tup) | 
 |  | 
 |     def __hash__(self): | 
 |         return self.hashvalue | 
 |  | 
 | def _make_key(args, kwds, typed, | 
 |              kwd_mark = (object(),), | 
 |              fasttypes = {int, str, frozenset, type(None)}, | 
 |              sorted=sorted, tuple=tuple, type=type, len=len): | 
 |     """Make a cache key from optionally typed positional and keyword arguments | 
 |  | 
 |     The key is constructed in a way that is flat as possible rather than | 
 |     as a nested structure that would take more memory. | 
 |  | 
 |     If there is only a single argument and its data type is known to cache | 
 |     its hash value, then that argument is returned without a wrapper.  This | 
 |     saves space and improves lookup speed. | 
 |  | 
 |     """ | 
 |     key = args | 
 |     if kwds: | 
 |         sorted_items = sorted(kwds.items()) | 
 |         key += kwd_mark | 
 |         for item in sorted_items: | 
 |             key += item | 
 |     if typed: | 
 |         key += tuple(type(v) for v in args) | 
 |         if kwds: | 
 |             key += tuple(type(v) for k, v in sorted_items) | 
 |     elif len(key) == 1 and type(key[0]) in fasttypes: | 
 |         return key[0] | 
 |     return _HashedSeq(key) | 
 |  | 
 | def lru_cache(maxsize=128, typed=False): | 
 |     """Least-recently-used cache decorator. | 
 |  | 
 |     If *maxsize* is set to None, the LRU features are disabled and the cache | 
 |     can grow without bound. | 
 |  | 
 |     If *typed* is True, arguments of different types will be cached separately. | 
 |     For example, f(3.0) and f(3) will be treated as distinct calls with | 
 |     distinct results. | 
 |  | 
 |     Arguments to the cached function must be hashable. | 
 |  | 
 |     View the cache statistics named tuple (hits, misses, maxsize, currsize) | 
 |     with f.cache_info().  Clear the cache and statistics with f.cache_clear(). | 
 |     Access the underlying function with f.__wrapped__. | 
 |  | 
 |     See:  http://en.wikipedia.org/wiki/Cache_algorithms#Least_Recently_Used | 
 |  | 
 |     """ | 
 |  | 
 |     # Users should only access the lru_cache through its public API: | 
 |     #       cache_info, cache_clear, and f.__wrapped__ | 
 |     # The internals of the lru_cache are encapsulated for thread safety and | 
 |     # to allow the implementation to change (including a possible C version). | 
 |  | 
 |     # Constants shared by all lru cache instances: | 
 |     sentinel = object()          # unique object used to signal cache misses | 
 |     make_key = _make_key         # build a key from the function arguments | 
 |     PREV, NEXT, KEY, RESULT = 0, 1, 2, 3   # names for the link fields | 
 |  | 
 |     def decorating_function(user_function): | 
 |         cache = {} | 
 |         hits = misses = 0 | 
 |         full = False | 
 |         cache_get = cache.get    # bound method to lookup a key or return None | 
 |         lock = RLock()           # because linkedlist updates aren't threadsafe | 
 |         root = []                # root of the circular doubly linked list | 
 |         root[:] = [root, root, None, None]     # initialize by pointing to self | 
 |  | 
 |         if maxsize == 0: | 
 |  | 
 |             def wrapper(*args, **kwds): | 
 |                 # No caching -- just a statistics update after a successful call | 
 |                 nonlocal misses | 
 |                 result = user_function(*args, **kwds) | 
 |                 misses += 1 | 
 |                 return result | 
 |  | 
 |         elif maxsize is None: | 
 |  | 
 |             def wrapper(*args, **kwds): | 
 |                 # Simple caching without ordering or size limit | 
 |                 nonlocal hits, misses | 
 |                 key = make_key(args, kwds, typed) | 
 |                 result = cache_get(key, sentinel) | 
 |                 if result is not sentinel: | 
 |                     hits += 1 | 
 |                     return result | 
 |                 result = user_function(*args, **kwds) | 
 |                 cache[key] = result | 
 |                 misses += 1 | 
 |                 return result | 
 |  | 
 |         else: | 
 |  | 
 |             def wrapper(*args, **kwds): | 
 |                 # Size limited caching that tracks accesses by recency | 
 |                 nonlocal root, hits, misses, full | 
 |                 key = make_key(args, kwds, typed) | 
 |                 with lock: | 
 |                     link = cache_get(key) | 
 |                     if link is not None: | 
 |                         # Move the link to the front of the circular queue | 
 |                         link_prev, link_next, _key, result = link | 
 |                         link_prev[NEXT] = link_next | 
 |                         link_next[PREV] = link_prev | 
 |                         last = root[PREV] | 
 |                         last[NEXT] = root[PREV] = link | 
 |                         link[PREV] = last | 
 |                         link[NEXT] = root | 
 |                         hits += 1 | 
 |                         return result | 
 |                 result = user_function(*args, **kwds) | 
 |                 with lock: | 
 |                     if key in cache: | 
 |                         # Getting here means that this same key was added to the | 
 |                         # cache while the lock was released.  Since the link | 
 |                         # update is already done, we need only return the | 
 |                         # computed result and update the count of misses. | 
 |                         pass | 
 |                     elif full: | 
 |                         # Use the old root to store the new key and result. | 
 |                         oldroot = root | 
 |                         oldroot[KEY] = key | 
 |                         oldroot[RESULT] = result | 
 |                         # Empty the oldest link and make it the new root. | 
 |                         # Keep a reference to the old key and old result to | 
 |                         # prevent their ref counts from going to zero during the | 
 |                         # update. That will prevent potentially arbitrary object | 
 |                         # clean-up code (i.e. __del__) from running while we're | 
 |                         # still adjusting the links. | 
 |                         root = oldroot[NEXT] | 
 |                         oldkey = root[KEY] | 
 |                         oldresult = root[RESULT] | 
 |                         root[KEY] = root[RESULT] = None | 
 |                         # Now update the cache dictionary. | 
 |                         del cache[oldkey] | 
 |                         # Save the potentially reentrant cache[key] assignment | 
 |                         # for last, after the root and links have been put in | 
 |                         # a consistent state. | 
 |                         cache[key] = oldroot | 
 |                     else: | 
 |                         # Put result in a new link at the front of the queue. | 
 |                         last = root[PREV] | 
 |                         link = [last, root, key, result] | 
 |                         last[NEXT] = root[PREV] = cache[key] = link | 
 |                         full = (len(cache) >= maxsize) | 
 |                     misses += 1 | 
 |                 return result | 
 |  | 
 |         def cache_info(): | 
 |             """Report cache statistics""" | 
 |             with lock: | 
 |                 return _CacheInfo(hits, misses, maxsize, len(cache)) | 
 |  | 
 |         def cache_clear(): | 
 |             """Clear the cache and cache statistics""" | 
 |             nonlocal hits, misses, full | 
 |             with lock: | 
 |                 cache.clear() | 
 |                 root[:] = [root, root, None, None] | 
 |                 hits = misses = 0 | 
 |                 full = False | 
 |  | 
 |         wrapper.cache_info = cache_info | 
 |         wrapper.cache_clear = cache_clear | 
 |         return update_wrapper(wrapper, user_function) | 
 |  | 
 |     return decorating_function | 
 |  | 
 |  | 
 | ################################################################################ | 
 | ### singledispatch() - single-dispatch generic function decorator | 
 | ################################################################################ | 
 |  | 
 | def _c3_merge(sequences): | 
 |     """Merges MROs in *sequences* to a single MRO using the C3 algorithm. | 
 |  | 
 |     Adapted from http://www.python.org/download/releases/2.3/mro/. | 
 |  | 
 |     """ | 
 |     result = [] | 
 |     while True: | 
 |         sequences = [s for s in sequences if s]   # purge empty sequences | 
 |         if not sequences: | 
 |             return result | 
 |         for s1 in sequences:   # find merge candidates among seq heads | 
 |             candidate = s1[0] | 
 |             for s2 in sequences: | 
 |                 if candidate in s2[1:]: | 
 |                     candidate = None | 
 |                     break      # reject the current head, it appears later | 
 |             else: | 
 |                 break | 
 |         if not candidate: | 
 |             raise RuntimeError("Inconsistent hierarchy") | 
 |         result.append(candidate) | 
 |         # remove the chosen candidate | 
 |         for seq in sequences: | 
 |             if seq[0] == candidate: | 
 |                 del seq[0] | 
 |  | 
 | def _c3_mro(cls, abcs=None): | 
 |     """Computes the method resolution order using extended C3 linearization. | 
 |  | 
 |     If no *abcs* are given, the algorithm works exactly like the built-in C3 | 
 |     linearization used for method resolution. | 
 |  | 
 |     If given, *abcs* is a list of abstract base classes that should be inserted | 
 |     into the resulting MRO. Unrelated ABCs are ignored and don't end up in the | 
 |     result. The algorithm inserts ABCs where their functionality is introduced, | 
 |     i.e. issubclass(cls, abc) returns True for the class itself but returns | 
 |     False for all its direct base classes. Implicit ABCs for a given class | 
 |     (either registered or inferred from the presence of a special method like | 
 |     __len__) are inserted directly after the last ABC explicitly listed in the | 
 |     MRO of said class. If two implicit ABCs end up next to each other in the | 
 |     resulting MRO, their ordering depends on the order of types in *abcs*. | 
 |  | 
 |     """ | 
 |     for i, base in enumerate(reversed(cls.__bases__)): | 
 |         if hasattr(base, '__abstractmethods__'): | 
 |             boundary = len(cls.__bases__) - i | 
 |             break   # Bases up to the last explicit ABC are considered first. | 
 |     else: | 
 |         boundary = 0 | 
 |     abcs = list(abcs) if abcs else [] | 
 |     explicit_bases = list(cls.__bases__[:boundary]) | 
 |     abstract_bases = [] | 
 |     other_bases = list(cls.__bases__[boundary:]) | 
 |     for base in abcs: | 
 |         if issubclass(cls, base) and not any( | 
 |                 issubclass(b, base) for b in cls.__bases__ | 
 |             ): | 
 |             # If *cls* is the class that introduces behaviour described by | 
 |             # an ABC *base*, insert said ABC to its MRO. | 
 |             abstract_bases.append(base) | 
 |     for base in abstract_bases: | 
 |         abcs.remove(base) | 
 |     explicit_c3_mros = [_c3_mro(base, abcs=abcs) for base in explicit_bases] | 
 |     abstract_c3_mros = [_c3_mro(base, abcs=abcs) for base in abstract_bases] | 
 |     other_c3_mros = [_c3_mro(base, abcs=abcs) for base in other_bases] | 
 |     return _c3_merge( | 
 |         [[cls]] + | 
 |         explicit_c3_mros + abstract_c3_mros + other_c3_mros + | 
 |         [explicit_bases] + [abstract_bases] + [other_bases] | 
 |     ) | 
 |  | 
 | def _compose_mro(cls, types): | 
 |     """Calculates the method resolution order for a given class *cls*. | 
 |  | 
 |     Includes relevant abstract base classes (with their respective bases) from | 
 |     the *types* iterable. Uses a modified C3 linearization algorithm. | 
 |  | 
 |     """ | 
 |     bases = set(cls.__mro__) | 
 |     # Remove entries which are already present in the __mro__ or unrelated. | 
 |     def is_related(typ): | 
 |         return (typ not in bases and hasattr(typ, '__mro__') | 
 |                                  and issubclass(cls, typ)) | 
 |     types = [n for n in types if is_related(n)] | 
 |     # Remove entries which are strict bases of other entries (they will end up | 
 |     # in the MRO anyway. | 
 |     def is_strict_base(typ): | 
 |         for other in types: | 
 |             if typ != other and typ in other.__mro__: | 
 |                 return True | 
 |         return False | 
 |     types = [n for n in types if not is_strict_base(n)] | 
 |     # Subclasses of the ABCs in *types* which are also implemented by | 
 |     # *cls* can be used to stabilize ABC ordering. | 
 |     type_set = set(types) | 
 |     mro = [] | 
 |     for typ in types: | 
 |         found = [] | 
 |         for sub in typ.__subclasses__(): | 
 |             if sub not in bases and issubclass(cls, sub): | 
 |                 found.append([s for s in sub.__mro__ if s in type_set]) | 
 |         if not found: | 
 |             mro.append(typ) | 
 |             continue | 
 |         # Favor subclasses with the biggest number of useful bases | 
 |         found.sort(key=len, reverse=True) | 
 |         for sub in found: | 
 |             for subcls in sub: | 
 |                 if subcls not in mro: | 
 |                     mro.append(subcls) | 
 |     return _c3_mro(cls, abcs=mro) | 
 |  | 
 | def _find_impl(cls, registry): | 
 |     """Returns the best matching implementation from *registry* for type *cls*. | 
 |  | 
 |     Where there is no registered implementation for a specific type, its method | 
 |     resolution order is used to find a more generic implementation. | 
 |  | 
 |     Note: if *registry* does not contain an implementation for the base | 
 |     *object* type, this function may return None. | 
 |  | 
 |     """ | 
 |     mro = _compose_mro(cls, registry.keys()) | 
 |     match = None | 
 |     for t in mro: | 
 |         if match is not None: | 
 |             # If *match* is an implicit ABC but there is another unrelated, | 
 |             # equally matching implicit ABC, refuse the temptation to guess. | 
 |             if (t in registry and t not in cls.__mro__ | 
 |                               and match not in cls.__mro__ | 
 |                               and not issubclass(match, t)): | 
 |                 raise RuntimeError("Ambiguous dispatch: {} or {}".format( | 
 |                     match, t)) | 
 |             break | 
 |         if t in registry: | 
 |             match = t | 
 |     return registry.get(match) | 
 |  | 
 | def singledispatch(func): | 
 |     """Single-dispatch generic function decorator. | 
 |  | 
 |     Transforms a function into a generic function, which can have different | 
 |     behaviours depending upon the type of its first argument. The decorated | 
 |     function acts as the default implementation, and additional | 
 |     implementations can be registered using the register() attribute of the | 
 |     generic function. | 
 |  | 
 |     """ | 
 |     registry = {} | 
 |     dispatch_cache = WeakKeyDictionary() | 
 |     cache_token = None | 
 |  | 
 |     def dispatch(cls): | 
 |         """generic_func.dispatch(cls) -> <function implementation> | 
 |  | 
 |         Runs the dispatch algorithm to return the best available implementation | 
 |         for the given *cls* registered on *generic_func*. | 
 |  | 
 |         """ | 
 |         nonlocal cache_token | 
 |         if cache_token is not None: | 
 |             current_token = get_cache_token() | 
 |             if cache_token != current_token: | 
 |                 dispatch_cache.clear() | 
 |                 cache_token = current_token | 
 |         try: | 
 |             impl = dispatch_cache[cls] | 
 |         except KeyError: | 
 |             try: | 
 |                 impl = registry[cls] | 
 |             except KeyError: | 
 |                 impl = _find_impl(cls, registry) | 
 |             dispatch_cache[cls] = impl | 
 |         return impl | 
 |  | 
 |     def register(cls, func=None): | 
 |         """generic_func.register(cls, func) -> func | 
 |  | 
 |         Registers a new implementation for the given *cls* on a *generic_func*. | 
 |  | 
 |         """ | 
 |         nonlocal cache_token | 
 |         if func is None: | 
 |             return lambda f: register(cls, f) | 
 |         registry[cls] = func | 
 |         if cache_token is None and hasattr(cls, '__abstractmethods__'): | 
 |             cache_token = get_cache_token() | 
 |         dispatch_cache.clear() | 
 |         return func | 
 |  | 
 |     def wrapper(*args, **kw): | 
 |         return dispatch(args[0].__class__)(*args, **kw) | 
 |  | 
 |     registry[object] = func | 
 |     wrapper.register = register | 
 |     wrapper.dispatch = dispatch | 
 |     wrapper.registry = MappingProxyType(registry) | 
 |     wrapper._clear_cache = dispatch_cache.clear | 
 |     update_wrapper(wrapper, func) | 
 |     return wrapper |