path: root/Lib/test/test_float.py

import unittest, struct
import os
from test import support
import math
from math import isinf, isnan, copysign, ldexp
import operator
import random, fractions

INF = float("inf")
NAN = float("nan")

class GeneralFloatCases(unittest.TestCase):

    def test_float(self):
        self.assertEqual(float(3.14), 3.14)
        self.assertEqual(float(314), 314.0)
        self.assertEqual(float("  3.14  "), 3.14)
        self.assertEqual(float(b" 3.14  "), 3.14)
        self.assertRaises(ValueError, float, "  0x3.1  ")
        self.assertRaises(ValueError, float, "  -0x3.p-1  ")
        self.assertRaises(ValueError, float, "  +0x3.p-1  ")
        self.assertRaises(ValueError, float, "++3.14")
        self.assertRaises(ValueError, float, "+-3.14")
        self.assertRaises(ValueError, float, "-+3.14")
        self.assertRaises(ValueError, float, "--3.14")
        self.assertEqual(float(b"  \u0663.\u0661\u0664  ".decode('raw-unicode-escape')), 3.14)

    @support.run_with_locale('LC_NUMERIC', 'fr_FR', 'de_DE')
    def test_float_with_comma(self):
        # set locale to something that doesn't use '.' for the decimal point
        # float must not accept the locale specific decimal point but
        # it still has to accept the normal python syntac
        import locale
        if not locale.localeconv()['decimal_point'] == ',':
            return

        self.assertEqual(float("  3.14  "), 3.14)
        self.assertEqual(float("+3.14  "), 3.14)
        self.assertEqual(float("-3.14  "), -3.14)
        self.assertEqual(float(".14  "), .14)
        self.assertEqual(float("3.  "), 3.0)
        self.assertEqual(float("3.e3  "), 3000.0)
        self.assertEqual(float("3.2e3  "), 3200.0)
        self.assertEqual(float("2.5e-1  "), 0.25)
        self.assertEqual(float("5e-1"), 0.5)
        self.assertRaises(ValueError, float, "  3,14  ")
        self.assertRaises(ValueError, float, "  +3,14  ")
        self.assertRaises(ValueError, float, "  -3,14  ")
        self.assertRaises(ValueError, float, "  0x3.1  ")
        self.assertRaises(ValueError, float, "  -0x3.p-1  ")
        self.assertRaises(ValueError, float, "  +0x3.p-1  ")
        self.assertEqual(float("  25.e-1  "), 2.5)
        self.assertEqual(support.fcmp(float("  .25e-1  "), .025), 0)

    def test_floatconversion(self):
        # Make sure that calls to __float__() work properly
        class Foo0:
            def __float__(self):
                return 42.

        class Foo1(object):
            def __float__(self):
                return 42.

        class Foo2(float):
            def __float__(self):
                return 42.

        class Foo3(float):
            def __new__(cls, value=0.):
                return float.__new__(cls, 2*value)

            def __float__(self):
                return self

        class Foo4(float):
            def __float__(self):
                return 42

        self.assertAlmostEqual(float(Foo0()), 42.)
        self.assertAlmostEqual(float(Foo1()), 42.)
        self.assertAlmostEqual(float(Foo2()), 42.)
        self.assertAlmostEqual(float(Foo3(21)), 42.)
        self.assertRaises(TypeError, float, Foo4(42))

    def test_floatasratio(self):
        for f, ratio in [
                (0.875, (7, 8)),
                (-0.875, (-7, 8)),
                (0.0, (0, 1)),
                (11.5, (23, 2)),
            ]:
            self.assertEqual(f.as_integer_ratio(), ratio)

        for i in range(10000):
            f = random.random()
            f *= 10 ** random.randint(-100, 100)
            n, d = f.as_integer_ratio()
            self.assertEqual(float(n).__truediv__(d), f)

        R = fractions.Fraction
        self.assertEqual(R(0, 1),
                         R(*float(0.0).as_integer_ratio()))
        self.assertEqual(R(5, 2),
                         R(*float(2.5).as_integer_ratio()))
        self.assertEqual(R(1, 2),
                         R(*float(0.5).as_integer_ratio()))
        self.assertEqual(R(4728779608739021, 2251799813685248),
                         R(*float(2.1).as_integer_ratio()))
        self.assertEqual(R(-4728779608739021, 2251799813685248),
                         R(*float(-2.1).as_integer_ratio()))
        self.assertEqual(R(-2100, 1),
                         R(*float(-2100.0).as_integer_ratio()))

        self.assertRaises(OverflowError, float('inf').as_integer_ratio)
        self.assertRaises(OverflowError, float('-inf').as_integer_ratio)
        self.assertRaises(ValueError, float('nan').as_integer_ratio)

class FormatFunctionsTestCase(unittest.TestCase):

    def setUp(self):
        self.save_formats = {'double':float.__getformat__('double'),
                             'float':float.__getformat__('float')}

    def tearDown(self):
        float.__setformat__('double', self.save_formats['double'])
        float.__setformat__('float', self.save_formats['float'])

    def test_getformat(self):
        self.assert_(float.__getformat__('double') in
                     ['unknown', 'IEEE, big-endian', 'IEEE, little-endian'])
        self.assert_(float.__getformat__('float') in
                     ['unknown', 'IEEE, big-endian', 'IEEE, little-endian'])
        self.assertRaises(ValueError, float.__getformat__, 'chicken')
        self.assertRaises(TypeError, float.__getformat__, 1)

    def test_setformat(self):
        for t in 'double', 'float':
            float.__setformat__(t, 'unknown')
            if self.save_formats[t] == 'IEEE, big-endian':
                self.assertRaises(ValueError, float.__setformat__,
                                  t, 'IEEE, little-endian')
            elif self.save_formats[t] == 'IEEE, little-endian':
                self.assertRaises(ValueError, float.__setformat__,
                                  t, 'IEEE, big-endian')
            else:
                self.assertRaises(ValueError, float.__setformat__,
                                  t, 'IEEE, big-endian')
                self.assertRaises(ValueError, float.__setformat__,
                                  t, 'IEEE, little-endian')
            self.assertRaises(ValueError, float.__setformat__,
                              t, 'chicken')
        self.assertRaises(ValueError, float.__setformat__,
                          'chicken', 'unknown')

BE_DOUBLE_INF = b'\x7f\xf0\x00\x00\x00\x00\x00\x00'
LE_DOUBLE_INF = bytes(reversed(BE_DOUBLE_INF))
BE_DOUBLE_NAN = b'\x7f\xf8\x00\x00\x00\x00\x00\x00'
LE_DOUBLE_NAN = bytes(reversed(BE_DOUBLE_NAN))

BE_FLOAT_INF = b'\x7f\x80\x00\x00'
LE_FLOAT_INF = bytes(reversed(BE_FLOAT_INF))
BE_FLOAT_NAN = b'\x7f\xc0\x00\x00'
LE_FLOAT_NAN = bytes(reversed(BE_FLOAT_NAN))

# on non-IEEE platforms, attempting to unpack a bit pattern
# representing an infinity or a NaN should raise an exception.

class UnknownFormatTestCase(unittest.TestCase):
    def setUp(self):
        self.save_formats = {'double':float.__getformat__('double'),
                             'float':float.__getformat__('float')}
        float.__setformat__('double', 'unknown')
        float.__setformat__('float', 'unknown')

    def tearDown(self):
        float.__setformat__('double', self.save_formats['double'])
        float.__setformat__('float', self.save_formats['float'])

    def test_double_specials_dont_unpack(self):
        for fmt, data in [('>d', BE_DOUBLE_INF),
                          ('>d', BE_DOUBLE_NAN),
                          ('<d', LE_DOUBLE_INF),
                          ('<d', LE_DOUBLE_NAN)]:
            self.assertRaises(ValueError, struct.unpack, fmt, data)

    def test_float_specials_dont_unpack(self):
        for fmt, data in [('>f', BE_FLOAT_INF),
                          ('>f', BE_FLOAT_NAN),
                          ('<f', LE_FLOAT_INF),
                          ('<f', LE_FLOAT_NAN)]:
            self.assertRaises(ValueError, struct.unpack, fmt, data)


# on an IEEE platform, all we guarantee is that bit patterns
# representing infinities or NaNs do not raise an exception; all else
# is accident (today).
# let's also try to guarantee that -0.0 and 0.0 don't get confused.

class IEEEFormatTestCase(unittest.TestCase):
    if float.__getformat__("double").startswith("IEEE"):
        def test_double_specials_do_unpack(self):
            for fmt, data in [('>d', BE_DOUBLE_INF),
                              ('>d', BE_DOUBLE_NAN),
                              ('<d', LE_DOUBLE_INF),
                              ('<d', LE_DOUBLE_NAN)]:
                struct.unpack(fmt, data)

    if float.__getformat__("float").startswith("IEEE"):
        def test_float_specials_do_unpack(self):
            for fmt, data in [('>f', BE_FLOAT_INF),
                              ('>f', BE_FLOAT_NAN),
                              ('<f', LE_FLOAT_INF),
                              ('<f', LE_FLOAT_NAN)]:
                struct.unpack(fmt, data)

    if float.__getformat__("double").startswith("IEEE"):
        def test_negative_zero(self):
            import math
            def pos_pos():
                return 0.0, math.atan2(0.0, -1)
            def pos_neg():
                return 0.0, math.atan2(-0.0, -1)
            def neg_pos():
                return -0.0, math.atan2(0.0, -1)
            def neg_neg():
                return -0.0, math.atan2(-0.0, -1) part[index2+1:]
        drv = root = ''
        if second == ':' and first in self.drive_letters:
            drv = part[:2]
            part = part[2:]
            first = third
        if first == sep:
            root = first
            part = part.lstrip(sep)
        return prefix + drv, root, part

    def casefold(self, s):
        return s.lower()

    def casefold_parts(self, parts):
        return [p.lower() for p in parts]

    def resolve(self, path):
        s = str(path)
        if not s:
            return os.getcwd()
        if _getfinalpathname is not None:
            return self._ext_to_normal(_getfinalpathname(s))
        # Means fallback on absolute
        return None

    def _split_extended_path(self, s, ext_prefix=ext_namespace_prefix):
        prefix = ''
        if s.startswith(ext_prefix):
            prefix = s[:4]
            s = s[4:]
            if s.startswith('UNC\\'):
                prefix += s[:3]
                s = '\\' + s[3:]
        return prefix, s

    def _ext_to_normal(self, s):
        # Turn back an extended path into a normal DOS-like path
        return self._split_extended_path(s)[1]

    def is_reserved(self, parts):
        # NOTE: the rules for reserved names seem somewhat complicated
        # (e.g. r"..\NUL" is reserved but not r"foo\NUL").
        # We err on the side of caution and return True for paths which are
        # not considered reserved by Windows.
        if not parts:
            return False
        if parts[0].startswith('\\\\'):
            # UNC paths are never reserved
            return False
        return parts[-1].partition('.')[0].upper() in self.reserved_names

    def make_uri(self, path):
        # Under Windows, file URIs use the UTF-8 encoding.
        drive = path.drive
        if len(drive) == 2 and drive[1] == ':':
            # It's a path on a local drive => 'file:///c:/a/b'
            rest = path.as_posix()[2:].lstrip('/')
            return 'file:///%s/%s' % (
                drive, urlquote_from_bytes(rest.encode('utf-8')))
        else:
            # It's a path on a network drive => 'file://host/share/a/b'
            return 'file:' + urlquote_from_bytes(path.as_posix().encode('utf-8'))

    def gethomedir(self, username):
        if 'HOME' in os.environ:
            userhome = os.environ['HOME']
        elif 'USERPROFILE' in os.environ:
            userhome = os.environ['USERPROFILE']
        elif 'HOMEPATH' in os.environ:
            try:
                drv = os.environ['HOMEDRIVE']
            except KeyError:
                drv = ''
            userhome = drv + os.environ['HOMEPATH']
        else:
            raise RuntimeError("Can't determine home directory")

        if username:
            # Try to guess user home directory.  By default all users
            # directories are located in the same place and are named by
            # corresponding usernames.  If current user home directory points
            # to nonstandard place, this guess is likely wrong.
            if os.environ['USERNAME'] != username:
                drv, root, parts = self.parse_parts((userhome,))
                if parts[-1] != os.environ['USERNAME']:
                    raise RuntimeError("Can't determine home directory "
                                       "for %r" % username)
                parts[-1] = username
                if drv or root:
                    userhome = drv + root + self.join(parts[1:])
                else:
                    userhome = self.join(parts)
        return userhome

class _PosixFlavour(_Flavour):
    sep = '/'
    altsep = ''
    has_drv = False
    pathmod = posixpath

    is_supported = (os.name != 'nt')

    def splitroot(self, part, sep=sep):
        if part and part[0] == sep:
            stripped_part = part.lstrip(sep)
            # According to POSIX path resolution:
            # http://pubs.opengroup.org/onlinepubs/009695399/basedefs/xbd_chap04.html#tag_04_11
            # "A pathname that begins with two successive slashes may be
            # interpreted in an implementation-defined manner, although more
            # than two leading slashes shall be treated as a single slash".
            if len(part) - len(stripped_part) == 2:
                return '', sep * 2, stripped_part
            else:
                return '', sep, stripped_part
        else:
            return '', '', part

    def casefold(self, s):
        return s

    def casefold_parts(self, parts):
        return parts

    def resolve(self, path):
        sep = self.sep
        accessor = path._accessor
        seen = {}
        def _resolve(path, rest):
            if rest.startswith(sep):
                path = ''

            for name in rest.split(sep):
                if not name or name == '.':
                    # current dir
                    continue
                if name == '..':
                    # parent dir
                    path, _, _ = path.rpartition(sep)
                    continue
                newpath = path + sep + name
                if newpath in seen:
                    # Already seen this path
                    path = seen[newpath]
                    if path is not None:
                        # use cached value
                        continue
                    # The symlink is not resolved, so we must have a symlink loop.
                    raise RuntimeError("Symlink loop from %r" % newpath)
                # Resolve the symbolic link
                try:
                    target = accessor.readlink(newpath)
                except OSError as e:
                    if e.errno != EINVAL:
                        raise
                    # Not a symlink
                    path = newpath
                else:
                    seen[newpath] = None # not resolved symlink
                    path = _resolve(path, target)
                    seen[newpath] = path # resolved symlink

            return path
        # NOTE: according to POSIX, getcwd() cannot contain path components
        # which are symlinks.
        base = '' if path.is_absolute() else os.getcwd()
        return _resolve(base, str(path)) or sep

    def is_reserved(self, parts):
        return False

    def make_uri(self, path):
        # We represent the path using the local filesystem encoding,
        # for portability to other applications.
        bpath = bytes(path)
        return 'file://' + urlquote_from_bytes(bpath)

    def gethomedir(self, username):
        if not username:
            try:
                return os.environ['HOME']
            except KeyError:
                import pwd
                return pwd.getpwuid(os.getuid()).pw_dir
        else:
            import pwd
            try:
                return pwd.getpwnam(username).pw_dir
            except KeyError:
                raise RuntimeError("Can't determine home directory "
                                   "for %r" % username)


_windows_flavour = _WindowsFlavour()
_posix_flavour = _PosixFlavour()


class _Accessor:
    """An accessor implements a particular (system-specific or not) way of
    accessing paths on the filesystem."""


class _NormalAccessor(_Accessor):

    def _wrap_strfunc(strfunc):
        @functools.wraps(strfunc)
        def wrapped(pathobj, *args):
            return strfunc(str(pathobj), *args)
        return staticmethod(wrapped)

    def _wrap_binary_strfunc(strfunc):
        @functools.wraps(strfunc)
        def wrapped(pathobjA, pathobjB, *args):
            return strfunc(str(pathobjA), str(pathobjB), *args)
        return staticmethod(wrapped)

    stat = _wrap_strfunc(os.stat)

    lstat = _wrap_strfunc(os.lstat)

    open = _wrap_strfunc(os.open)

    listdir = _wrap_strfunc(os.listdir)

    chmod = _wrap_strfunc(os.chmod)

    if hasattr(os, "lchmod"):
        lchmod = _wrap_strfunc(os.lchmod)
    else:
        def lchmod(self, pathobj, mode):
            raise NotImplementedError("lchmod() not available on this system")

    mkdir = _wrap_strfunc(os.mkdir)

    unlink = _wrap_strfunc(os.unlink)

    rmdir = _wrap_strfunc(os.rmdir)

    rename = _wrap_binary_strfunc(os.rename)

    replace = _wrap_binary_strfunc(os.replace)

    if nt:
        if supports_symlinks:
            symlink = _wrap_binary_strfunc(os.symlink)
        else:
            def symlink(a, b, target_is_directory):
                raise NotImplementedError("symlink() not available on this system")
    else:
        # Under POSIX, os.symlink() takes two args
        @staticmethod
        def symlink(a, b, target_is_directory):
            return os.symlink(str(a), str(b))

    utime = _wrap_strfunc(os.utime)

    # Helper for resolve()
    def readlink(self, path):
        return os.readlink(path)


_normal_accessor = _NormalAccessor()


#
# Globbing helpers
#

@contextmanager
def _cached(func):
    try:
        func.__cached__
        yield func
    except AttributeError:
        cache = {}
        def wrapper(*args):
            try:
                return cache[args]
            except KeyError:
                value = cache[args] = func(*args)
                return value
        wrapper.__cached__ = True
        try:
            yield wrapper
        finally:
            cache.clear()

def _make_selector(pattern_parts):
    pat = pattern_parts[0]
    child_parts = pattern_parts[1:]
    if pat == '**':
        cls = _RecursiveWildcardSelector
    elif '**' in pat:
        raise ValueError("Invalid pattern: '**' can only be an entire path component")
    elif _is_wildcard_pattern(pat):
        cls = _WildcardSelector
    else:
        cls = _PreciseSelector
    return cls(pat, child_parts)

if hasattr(functools, "lru_cache"):
    _make_selector = functools.lru_cache()(_make_selector)


class _Selector:
    """A selector matches a specific glob pattern part against the children
    of a given path."""

    def __init__(self, child_parts):
        self.child_parts = child_parts
        if child_parts:
            self.successor = _make_selector(child_parts)
        else:
            self.successor = _TerminatingSelector()

    def select_from(self, parent_path):
        """Iterate over all child paths of `parent_path` matched by this
        selector.  This can contain parent_path itself."""
        path_cls = type(parent_path)
        is_dir = path_cls.is_dir
        exists = path_cls.exists
        listdir = parent_path._accessor.listdir
        return self._select_from(parent_path, is_dir, exists, listdir)


class _TerminatingSelector:

    def _select_from(self, parent_path, is_dir, exists, listdir):
        yield parent_path


class _PreciseSelector(_Selector):

    def __init__(self, name, child_parts):
        self.name = name
        _Selector.__init__(self, child_parts)

    def _select_from(self, parent_path, is_dir, exists, listdir):
        try:
            if not is_dir(parent_path):
                return
            path = parent_path._make_child_relpath(self.name)
            if exists(path):
                for p in self.successor._select_from(path, is_dir, exists, listdir):
                    yield p
        except PermissionError:
            return


class _WildcardSelector(_Selector):

    def __init__(self, pat, child_parts):
        self.pat = re.compile(fnmatch.translate(pat))
        _Selector.__init__(self, child_parts)

    def _select_from(self, parent_path, is_dir, exists, listdir):
        try:
            if not is_dir(parent_path):
                return
            cf = parent_path._flavour.casefold
            for name in listdir(parent_path):
                casefolded = cf(name)
                if self.pat.match(casefolded):
                    path = parent_path._make_child_relpath(name)
                    for p in self.successor._select_from(path, is_dir, exists, listdir):
                        yield p
        except PermissionError:
            return



class _RecursiveWildcardSelector(_Selector):

    def __init__(self, pat, child_parts):
        _Selector.__init__(self, child_parts)

    def _iterate_directories(self, parent_path, is_dir, listdir):
        yield parent_path
        try:
            for name in listdir(parent_path):
                path = parent_path._make_child_relpath(name)
                if is_dir(path) and not path.is_symlink():
                    for p in self._iterate_directories(path, is_dir, listdir):
                        yield p
        except PermissionError:
            return

    def _select_from(self, parent_path, is_dir, exists, listdir):
        try:
            if not is_dir(parent_path):
                return
            with _cached(listdir) as listdir:
                yielded = set()
                try:
                    successor_select = self.successor._select_from
                    for starting_point in self._iterate_directories(parent_path, is_dir, listdir):
                        for p in successor_select(starting_point, is_dir, exists, listdir):
                            if p not in yielded:
                                yield p
                                yielded.add(p)
                finally:
                    yielded.clear()
        except PermissionError:
            return


#
# Public API
#

class _PathParents(Sequence):
    """This object provides sequence-like access to the logical ancestors
    of a path.  Don't try to construct it yourself."""
    __slots__ = ('_pathcls', '_drv', '_root', '_parts')

    def __init__(self, path):
        # We don't store the instance to avoid reference cycles
        self._pathcls = type(path)
        self._drv = path._drv
        self._root = path._root
        self._parts = path._parts

    def __len__(self):
        if self._drv or self._root:
            return len(self._parts) - 1
        else:
            return len(self._parts)

    def __getitem__(self, idx):
        if idx < 0 or idx >= len(self):
            raise IndexError(idx)
        return self._pathcls._from_parsed_parts(self._drv, self._root,
                                                self._parts[:-idx - 1])

    def __repr__(self):
        return "<{}.parents>".format(self._pathcls.__name__)


class PurePath(object):
    """PurePath represents a filesystem path and offers operations which
    don't imply any actual filesystem I/O.  Depending on your system,
    instantiating a PurePath will return either a PurePosixPath or a
    PureWindowsPath object.  You can also instantiate either of these classes
    directly, regardless of your system.
    """
    __slots__ = (
        '_drv', '_root', '_parts',
        '_str', '_hash', '_pparts', '_cached_cparts',
    )

    def __new__(cls, *args):
        """Construct a PurePath from one or several strings and or existing
        PurePath objects.  The strings and path objects are combined so as
        to yield a canonicalized path, which is incorporated into the
        new PurePath object.
        """
        if cls is PurePath:
            cls = PureWindowsPath if os.name == 'nt' else PurePosixPath
        return cls._from_parts(args)

    def __reduce__(self):
        # Using the parts tuple helps share interned path parts
        # when pickling related paths.
        return (self.__class__, tuple(self._parts))

    @classmethod
    def _parse_args(cls, args):
        # This is useful when you don't want to create an instance, just
        # canonicalize some constructor arguments.
        parts = []
        for a in args:
            if isinstance(a, PurePath):
                parts += a._parts
            else:
                a = os.fspath(a)
                if isinstance(a, str):
                    # Force-cast str subclasses to str (issue #21127)
                    parts.append(str(a))
                else:
                    raise TypeError(
                        "argument should be a str object or an os.PathLike "
                        "object returning str, not %r"
                        % type(a))
        return cls._flavour.parse_parts(parts)

    @classmethod
    def _from_parts(cls, args, init=True):
        # We need to call _parse_args on the instance, so as to get the
        # right flavour.
        self = object.__new__(cls)
        drv, root, parts = self._parse_args(args)
        self._drv = drv
        self._root = root
        self._parts = parts
        if init:
            self._init()
        return self

    @classmethod
    def _from_parsed_parts(cls, drv, root, parts, init=True):
        self = object.__new__(cls)
        self._drv = drv
        self._root = root
        self._parts = parts
        if init:
            self._init()
        return self

    @classmethod
    def _format_parsed_parts(cls, drv, root, parts):
        if drv or root:
            return drv + root + cls._flavour.join(parts[1:])
        else:
            return cls._flavour.join(parts)

    def _init(self):
        # Overridden in concrete Path
        pass

    def _make_child(self, args):
        drv, root, parts = self._parse_args(args)
        drv, root, parts = self._flavour.join_parsed_parts(
            self._drv, self._root, self._parts, drv, root, parts)
        return self._from_parsed_parts(drv, root, parts)

    def __str__(self):
        """Return the string representation of the path, suitable for
        passing to system calls."""
        try:
            return self._str
        except AttributeError:
            self._str = self._format_parsed_parts(self._drv, self._root,
                                                  self._parts) or '.'
            return self._str

    def __fspath__(self):
        return str(self)

    def as_posix(self):
        """Return the string representation of the path with forward (/)
        slashes."""
        f = self._flavour
        return str(self).replace(f.sep, '/')

    def __bytes__(self):
        """Return the bytes representation of the path.  This is only
        recommended to use under Unix."""
        return os.fsencode(str(self))

    def __repr__(self):
        return "{}({!r})".format(self.__class__.__name__, self.as_posix())

    def as_uri(self):
        """Return the path as a 'file' URI."""
        if not self.is_absolute():
            raise ValueError("relative path can't be expressed as a file URI")
        return self._flavour.make_uri(self)

    @property
    def _cparts(self):
        # Cached casefolded parts, for hashing and comparison
        try:
            return self._cached_cparts
        except AttributeError:
            self._cached_cparts = self._flavour.casefold_parts(self._parts)
            return self._cached_cparts

    def __eq__(self, other):
        if not isinstance(other, PurePath):
            return NotImplemented
        return self._cparts == other._cparts and self._flavour is other._flavour

    def __hash__(self):
        try:
            return self._hash
        except AttributeError:
            self._hash = hash(tuple(self._cparts))
            return self._hash

    def __lt__(self, other):
        if not isinstance(other, PurePath) or self._flavour is not other._flavour:
            return NotImplemented
        return self._cparts < other._cparts

    def __le__(self, other):
        if not isinstance(other, PurePath) or self._flavour is not other._flavour:
            return NotImplemented
        return self._cparts <= other._cparts

    def __gt__(self, other):
        if not isinstance(other, PurePath) or self._flavour is not other._flavour:
            return NotImplemented
        return self._cparts > other._cparts

    def __ge__(self, other):
        if not isinstance(other, PurePath) or self._flavour is not other._flavour:
            return NotImplemented
        return self._cparts >= other._cparts

    drive = property(attrgetter('_drv'),
                     doc="""The drive prefix (letter or UNC path), if any.""")

    root = property(attrgetter('_root'),
                    doc="""The root of the path, if any.""")

    @property
    def anchor(self):
        """The concatenation of the drive and root, or ''."""
        anchor = self._drv + self._root
        return anchor

    @property
    def name(self):
        """The final path component, if any."""
        parts = self._parts
        if len(parts) == (1 if (self._drv or self._root) else 0):
            return ''
        return parts[-1]

    @property
    def suffix(self):
        """The final component's last suffix, if any."""
        name = self.name
        i = name.rfind('.')
        if 0 < i < len(name) - 1:
            return name[i:]
        else:
            return ''

    @property
    def suffixes(self):
        """A list of the final component's suffixes, if any."""
        name = self.name
        if name.endswith('.'):
            return []
        name = name.lstrip('.')
        return ['.' + suffix for suffix in name.split('.')[1:]]

    @property
    def stem(self):
        """The final path component, minus its last suffix."""
        name = self.name
        i = name.rfind('.')
        if 0 < i < len(name) - 1:
            return name[:i]
        else:
            return name

    def with_name(self, name):
        """Return a new path with the file name changed."""
        if not self.name:
            raise ValueError("%r has an empty name" % (self,))
        drv, root, parts = self._flavour.parse_parts((name,))
        if (not name or name[-1] in [self._flavour.sep, self._flavour.altsep]
            or drv or root or len(parts) != 1):
            raise ValueError("Invalid name %r" % (name))
        return self._from_parsed_parts(self._drv, self._root,
                                       self._parts[:-1] + [name])

    def with_suffix(self, suffix):
        """Return a new path with the file suffix changed (or added, if none)."""
        # XXX if suffix is None, should the current suffix be removed?
        f = self._flavour
        if f.sep in suffix or f.altsep and f.altsep in suffix:
            raise ValueError("Invalid suffix %r" % (suffix))
        if suffix and not suffix.startswith('.') or suffix == '.':
            raise ValueError("Invalid suffix %r" % (suffix))
        name = self.name
        if not name:
            raise ValueError("%r has an empty name" % (self,))
        old_suffix = self.suffix
        if not old_suffix:
            name = name + suffix
        else:
            name = name[:-len(old_suffix)] + suffix
        return self._from_parsed_parts(self._drv, self._root,
                                       self._parts[:-1] + [name])

    def relative_to(self, *other):
        """Return the relative path to another path identified by the passed
        arguments.  If the operation is not possible (because this is not
        a subpath of the other path), raise ValueError.
        """
        # For the purpose of this method, drive and root are considered
        # separate parts, i.e.:
        #   Path('c:/').relative_to('c:')  gives Path('/')
        #   Path('c:/').relative_to('/')   raise ValueError
        if not other:
            raise TypeError("need at least one argument")
        parts = self._parts
        drv = self._drv
        root = self._root
        if root:
            abs_parts = [drv, root] + parts[1:]
        else:
            abs_parts = parts
        to_drv, to_root, to_parts = self._parse_args(other)
        if to_root:
            to_abs_parts = [to_drv, to_root] + to_parts[1:]
        else:
            to_abs_parts = to_parts
        n = len(to_abs_parts)
        cf = self._flavour.casefold_parts
        if (root or drv) if n == 0 else cf(abs_parts[:n]) != cf(to_abs_parts):
            formatted = self._format_parsed_parts(to_drv, to_root, to_parts)
            raise ValueError("{!r} does not start with {!r}"
                             .format(str(self), str(formatted)))
        return self._from_parsed_parts('', root if n == 1 else '',
                                       abs_parts[n:])

    @property
    def parts(self):
        """An object providing sequence-like access to the
        components in the filesystem path."""
        # We cache the tuple to avoid building a new one each time .parts
        # is accessed.  XXX is this necessary?
        try:
            return self._pparts
        except AttributeError:
            self._pparts = tuple(self._parts)
            return self._pparts

    def joinpath(self, *args):
        """Combine this path with one or several arguments, and return a
        new path representing either a subpath (if all arguments are relative
        paths) or a totally different path (if one of the arguments is
        anchored).
        """
        return self._make_child(args)

    def __truediv__(self, key):
        return self._make_child((key,))

    def __rtruediv__(self, key):
        return self._from_parts([key] + self._parts)

    @property
    def parent(self):
        """The logical parent of the path."""
        drv = self._drv
        root = self._root
        parts = self._parts
        if len(parts) == 1 and (drv or root):
            return self
        return self._from_parsed_parts(drv, root, parts[:-1])

    @property
    def parents(self):
        """A sequence of this path's logical parents."""
        return _PathParents(self)

    def is_absolute(self):
        """True if the path is absolute (has both a root and, if applicable,
        a drive)."""
        if not self._root:
            return False
        return not self._flavour.has_drv or bool(self._drv)

    def is_reserved(self):
        """Return True if the path contains one of the special names reserved
        by the system, if any."""
        return self._flavour.is_reserved(self._parts)

    def match(self, path_pattern):
        """
        Return True if this path matches the given pattern.
        """
        cf = self._flavour.casefold
        path_pattern = cf(path_pattern)
        drv, root, pat_parts = self._flavour.parse_parts((path_pattern,))
        if not pat_parts:
            raise ValueError("empty pattern")
        if drv and drv != cf(self._drv):
            return False
        if root and root != cf(self._root):
            return False
        parts = self._cparts
        if drv or root:
            if len(pat_parts) != len(parts):
                return False
            pat_parts = pat_parts[1:]
        elif len(pat_parts) > len(parts):
            return False
        for part, pat in zip(reversed(parts), reversed(pat_parts)):
            if not fnmatch.fnmatchcase(part, pat):
                return False
        return True

# Can't subclass os.PathLike from PurePath and keep the constructor
# optimizations in PurePath._parse_args().
os.PathLike.register(PurePath)


class PurePosixPath(PurePath):
    _flavour = _posix_flavour
    __slots__ = ()


class PureWindowsPath(PurePath):
    _flavour = _windows_flavour
    __slots__ = ()


# Filesystem-accessing classes


class Path(PurePath):
    __slots__ = (
        '_accessor',
        '_closed',
    )

    def __new__(cls, *args, **kwargs):
        if cls is Path:
            cls = WindowsPath if os.name == 'nt' else PosixPath
        self = cls._from_parts(args, init=False)
        if not self._flavour.is_supported:
            raise NotImplementedError("cannot instantiate %r on your system"
                                      % (cls.__name__,))
        self._init()
        return self

    def _init(self,
              # Private non-constructor arguments
              template=None,
              ):
        self._closed = False
        if template is not None:
            self._accessor = template._accessor
        else:
            self._accessor = _normal_accessor

    def _make_child_relpath(self, part):
        # This is an optimization used for dir walking.  `part` must be
        # a single part relative to this path.
        parts = self._parts + [part]
        return self._from_parsed_parts(self._drv, self._root, parts)

    def __enter__(self):
        if self._closed:
            self._raise_closed()
        return self

    def __exit__(self, t, v, tb):
        self._closed = True

    def _raise_closed(self):
        raise ValueError("I/O operation on closed path")

    def _opener(self, name, flags, mode=0o666):
        # A stub for the opener argument to built-in open()
        return self._accessor.open(self, flags, mode)

    def _raw_open(self, flags, mode=0o777):
        """
        Open the file pointed by this path and return a file descriptor,
        as os.open() does.
        """
        if self._closed:
            self._raise_closed()
        return self._accessor.open(self, flags, mode)

    # Public API

    @classmethod
    def cwd(cls):
        """Return a new path pointing to the current working directory
        (as returned by os.getcwd()).
        """
        return cls(os.getcwd())

    @classmethod
    def home(cls):
        """Return a new path pointing to the user's home directory (as
        returned by os.path.expanduser('~')).
        """
        return cls(cls()._flavour.gethomedir(None))

    def samefile(self, other_path):
        """Return whether other_path is the same or not as this file
        (as returned by os.path.samefile()).
        """
        st = self.stat()
        try:
            other_st = other_path.stat()
        except AttributeError:
            other_st = os.stat(other_path)
        return os.path.samestat(st, other_st)

    def iterdir(self):
        """Iterate over the files in this directory.  Does not yield any
        result for the special paths '.' and '..'.
        """
        if self._closed:
            self._raise_closed()
        for name in self._accessor.listdir(self):
            if name in {'.', '..'}:
                # Yielding a path object for these makes little sense
                continue
            yield self._make_child_relpath(name)
            if self._closed:
                self._raise_closed()

    def glob(self, pattern):
        """Iterate over this subtree and yield all existing files (of any
        kind, including directories) matching the given pattern.
        """
        if not pattern:
            raise ValueError("Unacceptable pattern: {!r}".format(pattern))
        pattern = self._flavour.casefold(pattern)
        drv, root, pattern_parts = self._flavour.parse_parts((pattern,))
        if drv or root:
            raise NotImplementedError("Non-relative patterns are unsupported")
        selector = _make_selector(tuple(pattern_parts))
        for p in selector.select_from(self):
            yield p

    def rglob(self, pattern):
        """Recursively yield all existing files (of any kind, including
        directories) matching the given pattern, anywhere in this subtree.
        """
        pattern = self._flavour.casefold(pattern)
        drv, root, pattern_parts = self._flavour.parse_parts((pattern,))
        if drv or root:
            raise NotImplementedError("Non-relative patterns are unsupported")
        selector = _make_selector(("**",) + tuple(pattern_parts))
        for p in selector.select_from(self):
            yield p

    def absolute(self):
        """Return an absolute version of this path.  This function works
        even if the path doesn't point to anything.

        No normalization is done, i.e. all '.' and '..' will be kept along.
        Use resolve() to get the canonical path to a file.
        """
        # XXX untested yet!
        if self._closed:
            self._raise_closed()
        if self.is_absolute():
            return self
        # FIXME this must defer to the specific flavour (and, under Windows,
        # use nt._getfullpathname())
        obj = self._from_parts([os.getcwd()] + self._parts, init=False)
        obj._init(template=self)
        return obj

    def resolve(self):
        """
        Make the path absolute, resolving all symlinks on the way and also
        normalizing it (for example turning slashes into backslashes under
        Windows).
        """
        if self._closed:
            self._raise_closed()
        s = self._flavour.resolve(self)
        if s is None:
            # No symlink resolution => for consistency, raise an error if
            # the path doesn't exist or is forbidden
            self.stat()
            s = str(self.absolute())
        # Now we have no symlinks in the path, it's safe to normalize it.
        normed = self._flavour.pathmod.normpath(s)
        obj = self._from_parts((normed,), init=False)
        obj._init(template=self)
        return obj

    def stat(self):
        """
        Return the result of the stat() system call on this path, like
        os.stat() does.
        """
        return self._accessor.stat(self)

    def owner(self):
        """
        Return the login name of the file owner.
        """
        import pwd
        return pwd.getpwuid(self.stat().st_uid).pw_name

    def group(self):
        """
        Return the group name of the file gid.
        """
        import grp
        return grp.getgrgid(self.stat().st_gid).gr_name

    def open(self, mode='r', buffering=-1, encoding=None,
             errors=None, newline=None):
        """
        Open the file pointed by this path and return a file object, as
        the built-in open() function does.
        """
        if self._closed:
            self._raise_closed()
        return io.open(str(self), mode, buffering, encoding, errors, newline,
                       opener=self._opener)

    def read_bytes(self):
        """
        Open the file in bytes mode, read it, and close the file.
        """
        with self.open(mode='rb') as f:
            return f.read()

    def read_text(self, encoding=None, errors=None):
        """
        Open the file in text mode, read it, and close the file.
        """
        with self.open(mode='r', encoding=encoding, errors=errors) as f:
            return f.read()

    def write_bytes(self, data):
        """
        Open the file in bytes mode, write to it, and close the file.
        """
        # type-check for the buffer interface before truncating the file
        view = memoryview(data)
        with self.open(mode='wb') as f:
            return f.write(view)

    def write_text(self, data, encoding=None, errors=None):
        """
        Open the file in text mode, write to it, and close the file.
        """
        if not isinstance(data, str):
            raise TypeError('data must be str, not %s' %
                            data.__class__.__name__)
        with self.open(mode='w', encoding=encoding, errors=errors) as f:
            return f.write(data)

    def touch(self, mode=0o666, exist_ok=True):
        """
        Create this file with the given access mode, if it doesn't exist.
        """
        if self._closed:
            self._raise_closed()
        if exist_ok:
            # First try to bump modification time
            # Implementation note: GNU touch uses the UTIME_NOW option of
            # the utimensat() / futimens() functions.
            try:
                self._accessor.utime(self, None)
            except OSError:
                # Avoid exception chaining
                pass
            else:
                return
        flags = os.O_CREAT | os.O_WRONLY
        if not exist_ok:
            flags |= os.O_EXCL
        fd = self._raw_open(flags, mode)
        os.close(fd)

    def mkdir(self, mode=0o777, parents=False, exist_ok=False):
        if self._closed:
            self._raise_closed()
        if not parents:
            try:
                self._accessor.mkdir(self, mode)
            except FileExistsError:
                if not exist_ok or not self.is_dir():
                    raise
        else:
            try:
                self._accessor.mkdir(self, mode)
            except FileExistsError:
                if not exist_ok or not self.is_dir():
                    raise
            except OSError as e:
                if e.errno != ENOENT:
                    raise
                self.parent.mkdir(parents=True)
                self._accessor.mkdir(self, mode)

    def chmod(self, mode):
        """
        Change the permissions of the path, like os.chmod().
        """
        if self._closed:
            self._raise_closed()
        self._accessor.chmod(self, mode)

    def lchmod(self, mode):
        """
        Like chmod(), except if the path points to a symlink, the symlink's
        permissions are changed, rather than its target's.
        """
        if self._closed:
            self._raise_closed()
        self._accessor.lchmod(self, mode)

    def unlink(self):
        """
        Remove this file or link.
        If the path is a directory, use rmdir() instead.
        """
        if self._closed:
            self._raise_closed()
        self._accessor.unlink(self)

    def rmdir(self):
        """
        Remove this directory.  The directory must be empty.
        """
        if self._closed:
            self._raise_closed()
        self._accessor.rmdir(self)

    def lstat(self):
        """
        Like stat(), except if the path points to a symlink, the symlink's
        status information is returned, rather than its target's.
        """
        if self._closed:
            self._raise_closed()
        return self._accessor.lstat(self)

    def rename(self, target):
        """
        Rename this path to the given path.
        """
        if self._closed:
            self._raise_closed()
        self._accessor.rename(self, target)

    def replace(self, target):
        """
        Rename this path to the given path, clobbering the existing
        destination if it exists.
        """
        if self._closed:
            self._raise_closed()
        self._accessor.replace(self, target)

    def symlink_to(self, target, target_is_directory=False):
        """
        Make this path a symlink pointing to the given path.
        Note the order of arguments (self, target) is the reverse of os.symlink's.
        """
        if self._closed:
            self._raise_closed()
        self._accessor.symlink(target, self, target_is_directory)

    # Convenience functions for querying the stat results

    def exists(self):
        """
        Whether this path exists.
        """
        try:
            self.stat()
        except OSError as e:
            if e.errno not in (ENOENT, ENOTDIR):
                raise
            return False
        return True

    def is_dir(self):
        """
        Whether this path is a directory.
        """
        try:
            return S_ISDIR(self.stat().st_mode)
        except OSError as e:
            if e.errno not in (ENOENT, ENOTDIR):
                raise
            # Path doesn't exist or is a broken symlink
            # (see https://bitbucket.org/pitrou/pathlib/issue/12/)
            return False

    def is_file(self):
        """
        Whether this path is a regular file (also True for symlinks pointing
        to regular files).
        """
        try:
            return S_ISREG(self.stat().st_mode)
        except OSError as e:
            if e.errno not in (ENOENT, ENOTDIR):
                raise
            # Path doesn't exist or is a broken symlink
            # (see https://bitbucket.org/pitrou/pathlib/issue/12/)
            return False

    def is_symlink(self):
        """
        Whether this path is a symbolic link.
        """
        try:
            return S_ISLNK(self.lstat().st_mode)
        except OSError as e:
            if e.errno not in (ENOENT, ENOTDIR):
                raise
            # Path doesn't exist
            return False

    def is_block_device(self):
        """
        Whether this path is a block device.
        """
        try:
            return S_ISBLK(self.stat().st_mode)
        except OSError as e:
            if e.errno not in (ENOENT, ENOTDIR):
                raise
            # Path doesn't exist or is a broken symlink
            # (see https://bitbucket.org/pitrou/pathlib/issue/12/)
            return False

    def is_char_device(self):
        """
        Whether this path is a character device.
        """
        try:
            return S_ISCHR(self.stat().st_mode)
        except OSError as e:
            if e.errno not in (ENOENT, ENOTDIR):
                raise
            # Path doesn't exist or is a broken symlink
            # (see https://bitbucket.org/pitrou/pathlib/issue/12/)
            return False

    def is_fifo(self):
        """
        Whether this path is a FIFO.
        """
        try:
            return S_ISFIFO(self.stat().st_mode)
        except OSError as e:
            if e.errno not in (ENOENT, ENOTDIR):
                raise
            # Path doesn't exist or is a broken symlink
            # (see https://bitbucket.org/pitrou/pathlib/issue/12/)
            return False

    def is_socket(self):
        """
        Whether this path is a socket.
        """
        try:
            return S_ISSOCK(self.stat().st_mode)
        except OSError as e:
            if e.errno not in (ENOENT, ENOTDIR):
                raise
            # Path doesn't exist or is a broken symlink
            # (see https://bitbucket.org/pitrou/pathlib/issue/12/)
            return False

    def expanduser(self):
        """ Return a new path with expanded ~ and ~user constructs
        (as returned by os.path.expanduser)
        """
        if (not (self._drv or self._root) and
            self._parts and self._parts[0][:1] == '~'):
            homedir = self._flavour.gethomedir(self._parts[0][1:])
            return self._from_parts([homedir] + self._parts[1:])

        return self


class PosixPath(Path, PurePosixPath):
    __slots__ = ()

class WindowsPath(Path, PureWindowsPath):
    __slots__ = ()

    def owner(self):
        raise NotImplementedError("Path.owner() is unsupported on this system")

    def group(self):
        raise NotImplementedError("Path.group() is unsupported on this system")