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ckpts/universal/global_step80/zero/16.input_layernorm.weight/exp_avg_sq.pt

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ckpts/universal/global_step80/zero/16.input_layernorm.weight/fp32.pt

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ckpts/universal/global_step80/zero/23.post_attention_layernorm.weight/exp_avg.pt

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ckpts/universal/global_step80/zero/23.post_attention_layernorm.weight/fp32.pt

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venv/lib/python3.10/site-packages/dateutil/parser/__init__.py

@@ -0,0 +1,61 @@
+# -*- coding: utf-8 -*-
+from ._parser import parse, parser, parserinfo, ParserError
+from ._parser import DEFAULTPARSER, DEFAULTTZPARSER
+from ._parser import UnknownTimezoneWarning
+
+from ._parser import __doc__
+
+from .isoparser import isoparser, isoparse
+
+__all__ = ['parse', 'parser', 'parserinfo',
+           'isoparse', 'isoparser',
+           'ParserError',
+           'UnknownTimezoneWarning']
+
+
+###
+# Deprecate portions of the private interface so that downstream code that
+# is improperly relying on it is given *some* notice.
+
+
+def __deprecated_private_func(f):
+    from functools import wraps
+    import warnings
+
+    msg = ('{name} is a private function and may break without warning, '
+           'it will be moved and or renamed in future versions.')
+    msg = msg.format(name=f.__name__)
+
+    @wraps(f)
+    def deprecated_func(*args, **kwargs):
+        warnings.warn(msg, DeprecationWarning)
+        return f(*args, **kwargs)
+
+    return deprecated_func
+
+def __deprecate_private_class(c):
+    import warnings
+
+    msg = ('{name} is a private class and may break without warning, '
+           'it will be moved and or renamed in future versions.')
+    msg = msg.format(name=c.__name__)
+
+    class private_class(c):
+        __doc__ = c.__doc__
+
+        def __init__(self, *args, **kwargs):
+            warnings.warn(msg, DeprecationWarning)
+            super(private_class, self).__init__(*args, **kwargs)
+
+    private_class.__name__ = c.__name__
+
+    return private_class
+
+
+from ._parser import _timelex, _resultbase
+from ._parser import _tzparser, _parsetz
+
+_timelex = __deprecate_private_class(_timelex)
+_tzparser = __deprecate_private_class(_tzparser)
+_resultbase = __deprecate_private_class(_resultbase)
+_parsetz = __deprecated_private_func(_parsetz)

venv/lib/python3.10/site-packages/dateutil/parser/_parser.py

@@ -0,0 +1,1613 @@
+# -*- coding: utf-8 -*-
+"""
+This module offers a generic date/time string parser which is able to parse
+most known formats to represent a date and/or time.
+
+This module attempts to be forgiving with regards to unlikely input formats,
+returning a datetime object even for dates which are ambiguous. If an element
+of a date/time stamp is omitted, the following rules are applied:
+
+- If AM or PM is left unspecified, a 24-hour clock is assumed, however, an hour
+  on a 12-hour clock (``0 <= hour <= 12``) *must* be specified if AM or PM is
+  specified.
+- If a time zone is omitted, a timezone-naive datetime is returned.
+
+If any other elements are missing, they are taken from the
+:class:`datetime.datetime` object passed to the parameter ``default``. If this
+results in a day number exceeding the valid number of days per month, the
+value falls back to the end of the month.
+
+Additional resources about date/time string formats can be found below:
+
+- `A summary of the international standard date and time notation
+  <https://www.cl.cam.ac.uk/~mgk25/iso-time.html>`_
+- `W3C Date and Time Formats <https://www.w3.org/TR/NOTE-datetime>`_
+- `Time Formats (Planetary Rings Node) <https://pds-rings.seti.org:443/tools/time_formats.html>`_
+- `CPAN ParseDate module
+  <https://metacpan.org/pod/release/MUIR/Time-modules-2013.0912/lib/Time/ParseDate.pm>`_
+- `Java SimpleDateFormat Class
+  <https://docs.oracle.com/javase/6/docs/api/java/text/SimpleDateFormat.html>`_
+"""
+from __future__ import unicode_literals
+
+import datetime
+import re
+import string
+import time
+import warnings
+
+from calendar import monthrange
+from io import StringIO
+
+import six
+from six import integer_types, text_type
+
+from decimal import Decimal
+
+from warnings import warn
+
+from .. import relativedelta
+from .. import tz
+
+__all__ = ["parse", "parserinfo", "ParserError"]
+
+
+# TODO: pandas.core.tools.datetimes imports this explicitly.  Might be worth
+# making public and/or figuring out if there is something we can
+# take off their plate.
+class _timelex(object):
+    # Fractional seconds are sometimes split by a comma
+    _split_decimal = re.compile("([.,])")
+
+    def __init__(self, instream):
+        if isinstance(instream, (bytes, bytearray)):
+            instream = instream.decode()
+
+        if isinstance(instream, text_type):
+            instream = StringIO(instream)
+        elif getattr(instream, 'read', None) is None:
+            raise TypeError('Parser must be a string or character stream, not '
+                            '{itype}'.format(itype=instream.__class__.__name__))
+
+        self.instream = instream
+        self.charstack = []
+        self.tokenstack = []
+        self.eof = False
+
+    def get_token(self):
+        """
+        This function breaks the time string into lexical units (tokens), which
+        can be parsed by the parser. Lexical units are demarcated by changes in
+        the character set, so any continuous string of letters is considered
+        one unit, any continuous string of numbers is considered one unit.
+
+        The main complication arises from the fact that dots ('.') can be used
+        both as separators (e.g. "Sep.20.2009") or decimal points (e.g.
+        "4:30:21.447"). As such, it is necessary to read the full context of
+        any dot-separated strings before breaking it into tokens; as such, this
+        function maintains a "token stack", for when the ambiguous context
+        demands that multiple tokens be parsed at once.
+        """
+        if self.tokenstack:
+            return self.tokenstack.pop(0)
+
+        seenletters = False
+        token = None
+        state = None
+
+        while not self.eof:
+            # We only realize that we've reached the end of a token when we
+            # find a character that's not part of the current token - since
+            # that character may be part of the next token, it's stored in the
+            # charstack.
+            if self.charstack:
+                nextchar = self.charstack.pop(0)
+            else:
+                nextchar = self.instream.read(1)
+                while nextchar == '\x00':
+                    nextchar = self.instream.read(1)
+
+            if not nextchar:
+                self.eof = True
+                break
+            elif not state:
+                # First character of the token - determines if we're starting
+                # to parse a word, a number or something else.
+                token = nextchar
+                if self.isword(nextchar):
+                    state = 'a'
+                elif self.isnum(nextchar):
+                    state = '0'
+                elif self.isspace(nextchar):
+                    token = ' '
+                    break  # emit token
+                else:
+                    break  # emit token
+            elif state == 'a':
+                # If we've already started reading a word, we keep reading
+                # letters until we find something that's not part of a word.
+                seenletters = True
+                if self.isword(nextchar):
+                    token += nextchar
+                elif nextchar == '.':
+                    token += nextchar
+                    state = 'a.'
+                else:
+                    self.charstack.append(nextchar)
+                    break  # emit token
+            elif state == '0':
+                # If we've already started reading a number, we keep reading
+                # numbers until we find something that doesn't fit.
+                if self.isnum(nextchar):
+                    token += nextchar
+                elif nextchar == '.' or (nextchar == ',' and len(token) >= 2):
+                    token += nextchar
+                    state = '0.'
+                else:
+                    self.charstack.append(nextchar)
+                    break  # emit token
+            elif state == 'a.':
+                # If we've seen some letters and a dot separator, continue
+                # parsing, and the tokens will be broken up later.
+                seenletters = True
+                if nextchar == '.' or self.isword(nextchar):
+                    token += nextchar
+                elif self.isnum(nextchar) and token[-1] == '.':
+                    token += nextchar
+                    state = '0.'
+                else:
+                    self.charstack.append(nextchar)
+                    break  # emit token
+            elif state == '0.':
+                # If we've seen at least one dot separator, keep going, we'll
+                # break up the tokens later.
+                if nextchar == '.' or self.isnum(nextchar):
+                    token += nextchar
+                elif self.isword(nextchar) and token[-1] == '.':
+                    token += nextchar
+                    state = 'a.'
+                else:
+                    self.charstack.append(nextchar)
+                    break  # emit token
+
+        if (state in ('a.', '0.') and (seenletters or token.count('.') > 1 or
+                                       token[-1] in '.,')):
+            l = self._split_decimal.split(token)
+            token = l[0]
+            for tok in l[1:]:
+                if tok:
+                    self.tokenstack.append(tok)
+
+        if state == '0.' and token.count('.') == 0:
+            token = token.replace(',', '.')
+
+        return token
+
+    def __iter__(self):
+        return self
+
+    def __next__(self):
+        token = self.get_token()
+        if token is None:
+            raise StopIteration
+
+        return token
+
+    def next(self):
+        return self.__next__()  # Python 2.x support
+
+    @classmethod
+    def split(cls, s):
+        return list(cls(s))
+
+    @classmethod
+    def isword(cls, nextchar):
+        """ Whether or not the next character is part of a word """
+        return nextchar.isalpha()
+
+    @classmethod
+    def isnum(cls, nextchar):
+        """ Whether the next character is part of a number """
+        return nextchar.isdigit()
+
+    @classmethod
+    def isspace(cls, nextchar):
+        """ Whether the next character is whitespace """
+        return nextchar.isspace()
+
+
+class _resultbase(object):
+
+    def __init__(self):
+        for attr in self.__slots__:
+            setattr(self, attr, None)
+
+    def _repr(self, classname):
+        l = []
+        for attr in self.__slots__:
+            value = getattr(self, attr)
+            if value is not None:
+                l.append("%s=%s" % (attr, repr(value)))
+        return "%s(%s)" % (classname, ", ".join(l))
+
+    def __len__(self):
+        return (sum(getattr(self, attr) is not None
+                    for attr in self.__slots__))
+
+    def __repr__(self):
+        return self._repr(self.__class__.__name__)
+
+
+class parserinfo(object):
+    """
+    Class which handles what inputs are accepted. Subclass this to customize
+    the language and acceptable values for each parameter.
+
+    :param dayfirst:
+        Whether to interpret the first value in an ambiguous 3-integer date
+        (e.g. 01/05/09) as the day (``True``) or month (``False``). If
+        ``yearfirst`` is set to ``True``, this distinguishes between YDM
+        and YMD. Default is ``False``.
+
+    :param yearfirst:
+        Whether to interpret the first value in an ambiguous 3-integer date
+        (e.g. 01/05/09) as the year. If ``True``, the first number is taken
+        to be the year, otherwise the last number is taken to be the year.
+        Default is ``False``.
+    """
+
+    # m from a.m/p.m, t from ISO T separator
+    JUMP = [" ", ".", ",", ";", "-", "/", "'",
+            "at", "on", "and", "ad", "m", "t", "of",
+            "st", "nd", "rd", "th"]
+
+    WEEKDAYS = [("Mon", "Monday"),
+                ("Tue", "Tuesday"),     # TODO: "Tues"
+                ("Wed", "Wednesday"),
+                ("Thu", "Thursday"),    # TODO: "Thurs"
+                ("Fri", "Friday"),
+                ("Sat", "Saturday"),
+                ("Sun", "Sunday")]
+    MONTHS = [("Jan", "January"),
+              ("Feb", "February"),      # TODO: "Febr"
+              ("Mar", "March"),
+              ("Apr", "April"),
+              ("May", "May"),
+              ("Jun", "June"),
+              ("Jul", "July"),
+              ("Aug", "August"),
+              ("Sep", "Sept", "September"),
+              ("Oct", "October"),
+              ("Nov", "November"),
+              ("Dec", "December")]
+    HMS = [("h", "hour", "hours"),
+           ("m", "minute", "minutes"),
+           ("s", "second", "seconds")]
+    AMPM = [("am", "a"),
+            ("pm", "p")]
+    UTCZONE = ["UTC", "GMT", "Z", "z"]
+    PERTAIN = ["of"]
+    TZOFFSET = {}
+    # TODO: ERA = ["AD", "BC", "CE", "BCE", "Stardate",
+    #              "Anno Domini", "Year of Our Lord"]
+
+    def __init__(self, dayfirst=False, yearfirst=False):
+        self._jump = self._convert(self.JUMP)
+        self._weekdays = self._convert(self.WEEKDAYS)
+        self._months = self._convert(self.MONTHS)
+        self._hms = self._convert(self.HMS)
+        self._ampm = self._convert(self.AMPM)
+        self._utczone = self._convert(self.UTCZONE)
+        self._pertain = self._convert(self.PERTAIN)
+
+        self.dayfirst = dayfirst
+        self.yearfirst = yearfirst
+
+        self._year = time.localtime().tm_year
+        self._century = self._year // 100 * 100
+
+    def _convert(self, lst):
+        dct = {}
+        for i, v in enumerate(lst):
+            if isinstance(v, tuple):
+                for v in v:
+                    dct[v.lower()] = i
+            else:
+                dct[v.lower()] = i
+        return dct
+
+    def jump(self, name):
+        return name.lower() in self._jump
+
+    def weekday(self, name):
+        try:
+            return self._weekdays[name.lower()]
+        except KeyError:
+            pass
+        return None
+
+    def month(self, name):
+        try:
+            return self._months[name.lower()] + 1
+        except KeyError:
+            pass
+        return None
+
+    def hms(self, name):
+        try:
+            return self._hms[name.lower()]
+        except KeyError:
+            return None
+
+    def ampm(self, name):
+        try:
+            return self._ampm[name.lower()]
+        except KeyError:
+            return None
+
+    def pertain(self, name):
+        return name.lower() in self._pertain
+
+    def utczone(self, name):
+        return name.lower() in self._utczone
+
+    def tzoffset(self, name):
+        if name in self._utczone:
+            return 0
+
+        return self.TZOFFSET.get(name)
+
+    def convertyear(self, year, century_specified=False):
+        """
+        Converts two-digit years to year within [-50, 49]
+        range of self._year (current local time)
+        """
+
+        # Function contract is that the year is always positive
+        assert year >= 0
+
+        if year < 100 and not century_specified:
+            # assume current century to start
+            year += self._century
+
+            if year >= self._year + 50:  # if too far in future
+                year -= 100
+            elif year < self._year - 50:  # if too far in past
+                year += 100
+
+        return year
+
+    def validate(self, res):
+        # move to info
+        if res.year is not None:
+            res.year = self.convertyear(res.year, res.century_specified)
+
+        if ((res.tzoffset == 0 and not res.tzname) or
+             (res.tzname == 'Z' or res.tzname == 'z')):
+            res.tzname = "UTC"
+            res.tzoffset = 0
+        elif res.tzoffset != 0 and res.tzname and self.utczone(res.tzname):
+            res.tzoffset = 0
+        return True
+
+
+class _ymd(list):
+    def __init__(self, *args, **kwargs):
+        super(self.__class__, self).__init__(*args, **kwargs)
+        self.century_specified = False
+        self.dstridx = None
+        self.mstridx = None
+        self.ystridx = None
+
+    @property
+    def has_year(self):
+        return self.ystridx is not None
+
+    @property
+    def has_month(self):
+        return self.mstridx is not None
+
+    @property
+    def has_day(self):
+        return self.dstridx is not None
+
+    def could_be_day(self, value):
+        if self.has_day:
+            return False
+        elif not self.has_month:
+            return 1 <= value <= 31
+        elif not self.has_year:
+            # Be permissive, assume leap year
+            month = self[self.mstridx]
+            return 1 <= value <= monthrange(2000, month)[1]
+        else:
+            month = self[self.mstridx]
+            year = self[self.ystridx]
+            return 1 <= value <= monthrange(year, month)[1]
+
+    def append(self, val, label=None):
+        if hasattr(val, '__len__'):
+            if val.isdigit() and len(val) > 2:
+                self.century_specified = True
+                if label not in [None, 'Y']:  # pragma: no cover
+                    raise ValueError(label)
+                label = 'Y'
+        elif val > 100:
+            self.century_specified = True
+            if label not in [None, 'Y']:  # pragma: no cover
+                raise ValueError(label)
+            label = 'Y'
+
+        super(self.__class__, self).append(int(val))
+
+        if label == 'M':
+            if self.has_month:
+                raise ValueError('Month is already set')
+            self.mstridx = len(self) - 1
+        elif label == 'D':
+            if self.has_day:
+                raise ValueError('Day is already set')
+            self.dstridx = len(self) - 1
+        elif label == 'Y':
+            if self.has_year:
+                raise ValueError('Year is already set')
+            self.ystridx = len(self) - 1
+
+    def _resolve_from_stridxs(self, strids):
+        """
+        Try to resolve the identities of year/month/day elements using
+        ystridx, mstridx, and dstridx, if enough of these are specified.
+        """
+        if len(self) == 3 and len(strids) == 2:
+            # we can back out the remaining stridx value
+            missing = [x for x in range(3) if x not in strids.values()]
+            key = [x for x in ['y', 'm', 'd'] if x not in strids]
+            assert len(missing) == len(key) == 1
+            key = key[0]
+            val = missing[0]
+            strids[key] = val
+
+        assert len(self) == len(strids)  # otherwise this should not be called
+        out = {key: self[strids[key]] for key in strids}
+        return (out.get('y'), out.get('m'), out.get('d'))
+
+    def resolve_ymd(self, yearfirst, dayfirst):
+        len_ymd = len(self)
+        year, month, day = (None, None, None)
+
+        strids = (('y', self.ystridx),
+                  ('m', self.mstridx),
+                  ('d', self.dstridx))
+
+        strids = {key: val for key, val in strids if val is not None}
+        if (len(self) == len(strids) > 0 or
+                (len(self) == 3 and len(strids) == 2)):
+            return self._resolve_from_stridxs(strids)
+
+        mstridx = self.mstridx
+
+        if len_ymd > 3:
+            raise ValueError("More than three YMD values")
+        elif len_ymd == 1 or (mstridx is not None and len_ymd == 2):
+            # One member, or two members with a month string
+            if mstridx is not None:
+                month = self[mstridx]
+                # since mstridx is 0 or 1, self[mstridx-1] always
+                # looks up the other element
+                other = self[mstridx - 1]
+            else:
+                other = self[0]
+
+            if len_ymd > 1 or mstridx is None:
+                if other > 31:
+                    year = other
+                else:
+                    day = other
+
+        elif len_ymd == 2:
+            # Two members with numbers
+            if self[0] > 31:
+                # 99-01
+                year, month = self
+            elif self[1] > 31:
+                # 01-99
+                month, year = self
+            elif dayfirst and self[1] <= 12:
+                # 13-01
+                day, month = self
+            else:
+                # 01-13
+                month, day = self
+
+        elif len_ymd == 3:
+            # Three members
+            if mstridx == 0:
+                if self[1] > 31:
+                    # Apr-2003-25
+                    month, year, day = self
+                else:
+                    month, day, year = self
+            elif mstridx == 1:
+                if self[0] > 31 or (yearfirst and self[2] <= 31):
+                    # 99-Jan-01
+                    year, month, day = self
+                else:
+                    # 01-Jan-01
+                    # Give precedence to day-first, since
+                    # two-digit years is usually hand-written.
+                    day, month, year = self
+
+            elif mstridx == 2:
+                # WTF!?
+                if self[1] > 31:
+                    # 01-99-Jan
+                    day, year, month = self
+                else:
+                    # 99-01-Jan
+                    year, day, month = self
+
+            else:
+                if (self[0] > 31 or
+                    self.ystridx == 0 or
+                        (yearfirst and self[1] <= 12 and self[2] <= 31)):
+                    # 99-01-01
+                    if dayfirst and self[2] <= 12:
+                        year, day, month = self
+                    else:
+                        year, month, day = self
+                elif self[0] > 12 or (dayfirst and self[1] <= 12):
+                    # 13-01-01
+                    day, month, year = self
+                else:
+                    # 01-13-01
+                    month, day, year = self
+
+        return year, month, day
+
+
+class parser(object):
+    def __init__(self, info=None):
+        self.info = info or parserinfo()
+
+    def parse(self, timestr, default=None,
+              ignoretz=False, tzinfos=None, **kwargs):
+        """
+        Parse the date/time string into a :class:`datetime.datetime` object.
+
+        :param timestr:
+            Any date/time string using the supported formats.
+
+        :param default:
+            The default datetime object, if this is a datetime object and not
+            ``None``, elements specified in ``timestr`` replace elements in the
+            default object.
+
+        :param ignoretz:
+            If set ``True``, time zones in parsed strings are ignored and a
+            naive :class:`datetime.datetime` object is returned.
+
+        :param tzinfos:
+            Additional time zone names / aliases which may be present in the
+            string. This argument maps time zone names (and optionally offsets
+            from those time zones) to time zones. This parameter can be a
+            dictionary with timezone aliases mapping time zone names to time
+            zones or a function taking two parameters (``tzname`` and
+            ``tzoffset``) and returning a time zone.
+
+            The timezones to which the names are mapped can be an integer
+            offset from UTC in seconds or a :class:`tzinfo` object.
+
+            .. doctest::
+               :options: +NORMALIZE_WHITESPACE
+
+                >>> from dateutil.parser import parse
+                >>> from dateutil.tz import gettz
+                >>> tzinfos = {"BRST": -7200, "CST": gettz("America/Chicago")}
+                >>> parse("2012-01-19 17:21:00 BRST", tzinfos=tzinfos)
+                datetime.datetime(2012, 1, 19, 17, 21, tzinfo=tzoffset(u'BRST', -7200))
+                >>> parse("2012-01-19 17:21:00 CST", tzinfos=tzinfos)
+                datetime.datetime(2012, 1, 19, 17, 21,
+                                  tzinfo=tzfile('/usr/share/zoneinfo/America/Chicago'))
+
+            This parameter is ignored if ``ignoretz`` is set.
+
+        :param \\*\\*kwargs:
+            Keyword arguments as passed to ``_parse()``.
+
+        :return:
+            Returns a :class:`datetime.datetime` object or, if the
+            ``fuzzy_with_tokens`` option is ``True``, returns a tuple, the
+            first element being a :class:`datetime.datetime` object, the second
+            a tuple containing the fuzzy tokens.
+
+        :raises ParserError:
+            Raised for invalid or unknown string format, if the provided
+            :class:`tzinfo` is not in a valid format, or if an invalid date
+            would be created.
+
+        :raises TypeError:
+            Raised for non-string or character stream input.
+
+        :raises OverflowError:
+            Raised if the parsed date exceeds the largest valid C integer on
+            your system.
+        """
+
+        if default is None:
+            default = datetime.datetime.now().replace(hour=0, minute=0,
+                                                      second=0, microsecond=0)
+
+        res, skipped_tokens = self._parse(timestr, **kwargs)
+
+        if res is None:
+            raise ParserError("Unknown string format: %s", timestr)
+
+        if len(res) == 0:
+            raise ParserError("String does not contain a date: %s", timestr)
+
+        try:
+            ret = self._build_naive(res, default)
+        except ValueError as e:
+            six.raise_from(ParserError(str(e) + ": %s", timestr), e)
+
+        if not ignoretz:
+            ret = self._build_tzaware(ret, res, tzinfos)
+
+        if kwargs.get('fuzzy_with_tokens', False):
+            return ret, skipped_tokens
+        else:
+            return ret
+
+    class _result(_resultbase):
+        __slots__ = ["year", "month", "day", "weekday",
+                     "hour", "minute", "second", "microsecond",
+                     "tzname", "tzoffset", "ampm","any_unused_tokens"]
+
+    def _parse(self, timestr, dayfirst=None, yearfirst=None, fuzzy=False,
+               fuzzy_with_tokens=False):
+        """
+        Private method which performs the heavy lifting of parsing, called from
+        ``parse()``, which passes on its ``kwargs`` to this function.
+
+        :param timestr:
+            The string to parse.
+
+        :param dayfirst:
+            Whether to interpret the first value in an ambiguous 3-integer date
+            (e.g. 01/05/09) as the day (``True``) or month (``False``). If
+            ``yearfirst`` is set to ``True``, this distinguishes between YDM
+            and YMD. If set to ``None``, this value is retrieved from the
+            current :class:`parserinfo` object (which itself defaults to
+            ``False``).
+
+        :param yearfirst:
+            Whether to interpret the first value in an ambiguous 3-integer date
+            (e.g. 01/05/09) as the year. If ``True``, the first number is taken
+            to be the year, otherwise the last number is taken to be the year.
+            If this is set to ``None``, the value is retrieved from the current
+            :class:`parserinfo` object (which itself defaults to ``False``).
+
+        :param fuzzy:
+            Whether to allow fuzzy parsing, allowing for string like "Today is
+            January 1, 2047 at 8:21:00AM".
+
+        :param fuzzy_with_tokens:
+            If ``True``, ``fuzzy`` is automatically set to True, and the parser
+            will return a tuple where the first element is the parsed
+            :class:`datetime.datetime` datetimestamp and the second element is
+            a tuple containing the portions of the string which were ignored:
+
+            .. doctest::
+
+                >>> from dateutil.parser import parse
+                >>> parse("Today is January 1, 2047 at 8:21:00AM", fuzzy_with_tokens=True)
+                (datetime.datetime(2047, 1, 1, 8, 21), (u'Today is ', u' ', u'at '))
+
+        """
+        if fuzzy_with_tokens:
+            fuzzy = True
+
+        info = self.info
+
+        if dayfirst is None:
+            dayfirst = info.dayfirst
+
+        if yearfirst is None:
+            yearfirst = info.yearfirst
+
+        res = self._result()
+        l = _timelex.split(timestr)         # Splits the timestr into tokens
+
+        skipped_idxs = []
+
+        # year/month/day list
+        ymd = _ymd()
+
+        len_l = len(l)
+        i = 0
+        try:
+            while i < len_l:
+
+                # Check if it's a number
+                value_repr = l[i]
+                try:
+                    value = float(value_repr)
+                except ValueError:
+                    value = None
+
+                if value is not None:
+                    # Numeric token
+                    i = self._parse_numeric_token(l, i, info, ymd, res, fuzzy)
+
+                # Check weekday
+                elif info.weekday(l[i]) is not None:
+                    value = info.weekday(l[i])
+                    res.weekday = value
+
+                # Check month name
+                elif info.month(l[i]) is not None:
+                    value = info.month(l[i])
+                    ymd.append(value, 'M')
+
+                    if i + 1 < len_l:
+                        if l[i + 1] in ('-', '/'):
+                            # Jan-01[-99]
+                            sep = l[i + 1]
+                            ymd.append(l[i + 2])
+
+                            if i + 3 < len_l and l[i + 3] == sep:
+                                # Jan-01-99
+                                ymd.append(l[i + 4])
+                                i += 2
+
+                            i += 2
+
+                        elif (i + 4 < len_l and l[i + 1] == l[i + 3] == ' ' and
+                              info.pertain(l[i + 2])):
+                            # Jan of 01
+                            # In this case, 01 is clearly year
+                            if l[i + 4].isdigit():
+                                # Convert it here to become unambiguous
+                                value = int(l[i + 4])
+                                year = str(info.convertyear(value))
+                                ymd.append(year, 'Y')
+                            else:
+                                # Wrong guess
+                                pass
+                                # TODO: not hit in tests
+                            i += 4
+
+                # Check am/pm
+                elif info.ampm(l[i]) is not None:
+                    value = info.ampm(l[i])
+                    val_is_ampm = self._ampm_valid(res.hour, res.ampm, fuzzy)
+
+                    if val_is_ampm:
+                        res.hour = self._adjust_ampm(res.hour, value)
+                        res.ampm = value
+
+                    elif fuzzy:
+                        skipped_idxs.append(i)
+
+                # Check for a timezone name
+                elif self._could_be_tzname(res.hour, res.tzname, res.tzoffset, l[i]):
+                    res.tzname = l[i]
+                    res.tzoffset = info.tzoffset(res.tzname)
+
+                    # Check for something like GMT+3, or BRST+3. Notice
+                    # that it doesn't mean "I am 3 hours after GMT", but
+                    # "my time +3 is GMT". If found, we reverse the
+                    # logic so that timezone parsing code will get it
+                    # right.
+                    if i + 1 < len_l and l[i + 1] in ('+', '-'):
+                        l[i + 1] = ('+', '-')[l[i + 1] == '+']
+                        res.tzoffset = None
+                        if info.utczone(res.tzname):
+                            # With something like GMT+3, the timezone
+                            # is *not* GMT.
+                            res.tzname = None
+
+                # Check for a numbered timezone
+                elif res.hour is not None and l[i] in ('+', '-'):
+                    signal = (-1, 1)[l[i] == '+']
+                    len_li = len(l[i + 1])
+
+                    # TODO: check that l[i + 1] is integer?
+                    if len_li == 4:
+                        # -0300
+                        hour_offset = int(l[i + 1][:2])
+                        min_offset = int(l[i + 1][2:])
+                    elif i + 2 < len_l and l[i + 2] == ':':
+                        # -03:00
+                        hour_offset = int(l[i + 1])
+                        min_offset = int(l[i + 3])  # TODO: Check that l[i+3] is minute-like?
+                        i += 2
+                    elif len_li <= 2:
+                        # -[0]3
+                        hour_offset = int(l[i + 1][:2])
+                        min_offset = 0
+                    else:
+                        raise ValueError(timestr)
+
+                    res.tzoffset = signal * (hour_offset * 3600 + min_offset * 60)
+
+                    # Look for a timezone name between parenthesis
+                    if (i + 5 < len_l and
+                            info.jump(l[i + 2]) and l[i + 3] == '(' and
+                            l[i + 5] == ')' and
+                            3 <= len(l[i + 4]) and
+                            self._could_be_tzname(res.hour, res.tzname,
+                                                  None, l[i + 4])):
+                        # -0300 (BRST)
+                        res.tzname = l[i + 4]
+                        i += 4
+
+                    i += 1
+
+                # Check jumps
+                elif not (info.jump(l[i]) or fuzzy):
+                    raise ValueError(timestr)
+
+                else:
+                    skipped_idxs.append(i)
+                i += 1
+
+            # Process year/month/day
+            year, month, day = ymd.resolve_ymd(yearfirst, dayfirst)
+
+            res.century_specified = ymd.century_specified
+            res.year = year
+            res.month = month
+            res.day = day
+
+        except (IndexError, ValueError):
+            return None, None
+
+        if not info.validate(res):
+            return None, None
+
+        if fuzzy_with_tokens:
+            skipped_tokens = self._recombine_skipped(l, skipped_idxs)
+            return res, tuple(skipped_tokens)
+        else:
+            return res, None
+
+    def _parse_numeric_token(self, tokens, idx, info, ymd, res, fuzzy):
+        # Token is a number
+        value_repr = tokens[idx]
+        try:
+            value = self._to_decimal(value_repr)
+        except Exception as e:
+            six.raise_from(ValueError('Unknown numeric token'), e)
+
+        len_li = len(value_repr)
+
+        len_l = len(tokens)
+
+        if (len(ymd) == 3 and len_li in (2, 4) and
+            res.hour is None and
+            (idx + 1 >= len_l or
+             (tokens[idx + 1] != ':' and
+              info.hms(tokens[idx + 1]) is None))):
+            # 19990101T23[59]
+            s = tokens[idx]
+            res.hour = int(s[:2])
+
+            if len_li == 4:
+                res.minute = int(s[2:])
+
+        elif len_li == 6 or (len_li > 6 and tokens[idx].find('.') == 6):
+            # YYMMDD or HHMMSS[.ss]
+            s = tokens[idx]
+
+            if not ymd and '.' not in tokens[idx]:
+                ymd.append(s[:2])
+                ymd.append(s[2:4])
+                ymd.append(s[4:])
+            else:
+                # 19990101T235959[.59]
+
+                # TODO: Check if res attributes already set.
+                res.hour = int(s[:2])
+                res.minute = int(s[2:4])
+                res.second, res.microsecond = self._parsems(s[4:])
+
+        elif len_li in (8, 12, 14):
+            # YYYYMMDD
+            s = tokens[idx]
+            ymd.append(s[:4], 'Y')
+            ymd.append(s[4:6])
+            ymd.append(s[6:8])
+
+            if len_li > 8:
+                res.hour = int(s[8:10])
+                res.minute = int(s[10:12])
+
+                if len_li > 12:
+                    res.second = int(s[12:])
+
+        elif self._find_hms_idx(idx, tokens, info, allow_jump=True) is not None:
+            # HH[ ]h or MM[ ]m or SS[.ss][ ]s
+            hms_idx = self._find_hms_idx(idx, tokens, info, allow_jump=True)
+            (idx, hms) = self._parse_hms(idx, tokens, info, hms_idx)
+            if hms is not None:
+                # TODO: checking that hour/minute/second are not
+                # already set?
+                self._assign_hms(res, value_repr, hms)
+
+        elif idx + 2 < len_l and tokens[idx + 1] == ':':
+            # HH:MM[:SS[.ss]]
+            res.hour = int(value)
+            value = self._to_decimal(tokens[idx + 2])  # TODO: try/except for this?
+            (res.minute, res.second) = self._parse_min_sec(value)
+
+            if idx + 4 < len_l and tokens[idx + 3] == ':':
+                res.second, res.microsecond = self._parsems(tokens[idx + 4])
+
+                idx += 2
+
+            idx += 2
+
+        elif idx + 1 < len_l and tokens[idx + 1] in ('-', '/', '.'):
+            sep = tokens[idx + 1]
+            ymd.append(value_repr)
+
+            if idx + 2 < len_l and not info.jump(tokens[idx + 2]):
+                if tokens[idx + 2].isdigit():
+                    # 01-01[-01]
+                    ymd.append(tokens[idx + 2])
+                else:
+                    # 01-Jan[-01]
+                    value = info.month(tokens[idx + 2])
+
+                    if value is not None:
+                        ymd.append(value, 'M')
+                    else:
+                        raise ValueError()
+
+                if idx + 3 < len_l and tokens[idx + 3] == sep:
+                    # We have three members
+                    value = info.month(tokens[idx + 4])
+
+                    if value is not None:
+                        ymd.append(value, 'M')
+                    else:
+                        ymd.append(tokens[idx + 4])
+                    idx += 2
+
+                idx += 1
+            idx += 1
+
+        elif idx + 1 >= len_l or info.jump(tokens[idx + 1]):
+            if idx + 2 < len_l and info.ampm(tokens[idx + 2]) is not None:
+                # 12 am
+                hour = int(value)
+                res.hour = self._adjust_ampm(hour, info.ampm(tokens[idx + 2]))
+                idx += 1
+            else:
+                # Year, month or day
+                ymd.append(value)
+            idx += 1
+
+        elif info.ampm(tokens[idx + 1]) is not None and (0 <= value < 24):
+            # 12am
+            hour = int(value)
+            res.hour = self._adjust_ampm(hour, info.ampm(tokens[idx + 1]))
+            idx += 1
+
+        elif ymd.could_be_day(value):
+            ymd.append(value)
+
+        elif not fuzzy:
+            raise ValueError()
+
+        return idx
+
+    def _find_hms_idx(self, idx, tokens, info, allow_jump):
+        len_l = len(tokens)
+
+        if idx+1 < len_l and info.hms(tokens[idx+1]) is not None:
+            # There is an "h", "m", or "s" label following this token.  We take
+            # assign the upcoming label to the current token.
+            # e.g. the "12" in 12h"
+            hms_idx = idx + 1
+
+        elif (allow_jump and idx+2 < len_l and tokens[idx+1] == ' ' and
+              info.hms(tokens[idx+2]) is not None):
+            # There is a space and then an "h", "m", or "s" label.
+            # e.g. the "12" in "12 h"
+            hms_idx = idx + 2
+
+        elif idx > 0 and info.hms(tokens[idx-1]) is not None:
+            # There is a "h", "m", or "s" preceding this token.  Since neither
+            # of the previous cases was hit, there is no label following this
+            # token, so we use the previous label.
+            # e.g. the "04" in "12h04"
+            hms_idx = idx-1
+
+        elif (1 < idx == len_l-1 and tokens[idx-1] == ' ' and
+              info.hms(tokens[idx-2]) is not None):
+            # If we are looking at the final token, we allow for a
+            # backward-looking check to skip over a space.
+            # TODO: Are we sure this is the right condition here?
+            hms_idx = idx - 2
+
+        else:
+            hms_idx = None
+
+        return hms_idx
+
+    def _assign_hms(self, res, value_repr, hms):
+        # See GH issue #427, fixing float rounding
+        value = self._to_decimal(value_repr)
+
+        if hms == 0:
+            # Hour
+            res.hour = int(value)
+            if value % 1:
+                res.minute = int(60*(value % 1))
+
+        elif hms == 1:
+            (res.minute, res.second) = self._parse_min_sec(value)
+
+        elif hms == 2:
+            (res.second, res.microsecond) = self._parsems(value_repr)
+
+    def _could_be_tzname(self, hour, tzname, tzoffset, token):
+        return (hour is not None and
+                tzname is None and
+                tzoffset is None and
+                len(token) <= 5 and
+                (all(x in string.ascii_uppercase for x in token)
+                 or token in self.info.UTCZONE))
+
+    def _ampm_valid(self, hour, ampm, fuzzy):
+        """
+        For fuzzy parsing, 'a' or 'am' (both valid English words)
+        may erroneously trigger the AM/PM flag. Deal with that
+        here.
+        """
+        val_is_ampm = True
+
+        # If there's already an AM/PM flag, this one isn't one.
+        if fuzzy and ampm is not None:
+            val_is_ampm = False
+
+        # If AM/PM is found and hour is not, raise a ValueError
+        if hour is None:
+            if fuzzy:
+                val_is_ampm = False
+            else:
+                raise ValueError('No hour specified with AM or PM flag.')
+        elif not 0 <= hour <= 12:
+            # If AM/PM is found, it's a 12 hour clock, so raise
+            # an error for invalid range
+            if fuzzy:
+                val_is_ampm = False
+            else:
+                raise ValueError('Invalid hour specified for 12-hour clock.')
+
+        return val_is_ampm
+
+    def _adjust_ampm(self, hour, ampm):
+        if hour < 12 and ampm == 1:
+            hour += 12
+        elif hour == 12 and ampm == 0:
+            hour = 0
+        return hour
+
+    def _parse_min_sec(self, value):
+        # TODO: Every usage of this function sets res.second to the return
+        # value. Are there any cases where second will be returned as None and
+        # we *don't* want to set res.second = None?
+        minute = int(value)
+        second = None
+
+        sec_remainder = value % 1
+        if sec_remainder:
+            second = int(60 * sec_remainder)
+        return (minute, second)
+
+    def _parse_hms(self, idx, tokens, info, hms_idx):
+        # TODO: Is this going to admit a lot of false-positives for when we
+        # just happen to have digits and "h", "m" or "s" characters in non-date
+        # text?  I guess hex hashes won't have that problem, but there's plenty
+        # of random junk out there.
+        if hms_idx is None:
+            hms = None
+            new_idx = idx
+        elif hms_idx > idx:
+            hms = info.hms(tokens[hms_idx])
+            new_idx = hms_idx
+        else:
+            # Looking backwards, increment one.
+            hms = info.hms(tokens[hms_idx]) + 1
+            new_idx = idx
+
+        return (new_idx, hms)
+
+    # ------------------------------------------------------------------
+    # Handling for individual tokens.  These are kept as methods instead
+    #  of functions for the sake of customizability via subclassing.
+
+    def _parsems(self, value):
+        """Parse a I[.F] seconds value into (seconds, microseconds)."""
+        if "." not in value:
+            return int(value), 0
+        else:
+            i, f = value.split(".")
+            return int(i), int(f.ljust(6, "0")[:6])
+
+    def _to_decimal(self, val):
+        try:
+            decimal_value = Decimal(val)
+            # See GH 662, edge case, infinite value should not be converted
+            #  via `_to_decimal`
+            if not decimal_value.is_finite():
+                raise ValueError("Converted decimal value is infinite or NaN")
+        except Exception as e:
+            msg = "Could not convert %s to decimal" % val
+            six.raise_from(ValueError(msg), e)
+        else:
+            return decimal_value
+
+    # ------------------------------------------------------------------
+    # Post-Parsing construction of datetime output.  These are kept as
+    #  methods instead of functions for the sake of customizability via
+    #  subclassing.
+
+    def _build_tzinfo(self, tzinfos, tzname, tzoffset):
+        if callable(tzinfos):
+            tzdata = tzinfos(tzname, tzoffset)
+        else:
+            tzdata = tzinfos.get(tzname)
+        # handle case where tzinfo is paased an options that returns None
+        # eg tzinfos = {'BRST' : None}
+        if isinstance(tzdata, datetime.tzinfo) or tzdata is None:
+            tzinfo = tzdata
+        elif isinstance(tzdata, text_type):
+            tzinfo = tz.tzstr(tzdata)
+        elif isinstance(tzdata, integer_types):
+            tzinfo = tz.tzoffset(tzname, tzdata)
+        else:
+            raise TypeError("Offset must be tzinfo subclass, tz string, "
+                            "or int offset.")
+        return tzinfo
+
+    def _build_tzaware(self, naive, res, tzinfos):
+        if (callable(tzinfos) or (tzinfos and res.tzname in tzinfos)):
+            tzinfo = self._build_tzinfo(tzinfos, res.tzname, res.tzoffset)
+            aware = naive.replace(tzinfo=tzinfo)
+            aware = self._assign_tzname(aware, res.tzname)
+
+        elif res.tzname and res.tzname in time.tzname:
+            aware = naive.replace(tzinfo=tz.tzlocal())
+
+            # Handle ambiguous local datetime
+            aware = self._assign_tzname(aware, res.tzname)
+
+            # This is mostly relevant for winter GMT zones parsed in the UK
+            if (aware.tzname() != res.tzname and
+                    res.tzname in self.info.UTCZONE):
+                aware = aware.replace(tzinfo=tz.UTC)
+
+        elif res.tzoffset == 0:
+            aware = naive.replace(tzinfo=tz.UTC)
+
+        elif res.tzoffset:
+            aware = naive.replace(tzinfo=tz.tzoffset(res.tzname, res.tzoffset))
+
+        elif not res.tzname and not res.tzoffset:
+            # i.e. no timezone information was found.
+            aware = naive
+
+        elif res.tzname:
+            # tz-like string was parsed but we don't know what to do
+            # with it
+            warnings.warn("tzname {tzname} identified but not understood.  "
+                          "Pass `tzinfos` argument in order to correctly "
+                          "return a timezone-aware datetime.  In a future "
+                          "version, this will raise an "
+                          "exception.".format(tzname=res.tzname),
+                          category=UnknownTimezoneWarning)
+            aware = naive
+
+        return aware
+
+    def _build_naive(self, res, default):
+        repl = {}
+        for attr in ("year", "month", "day", "hour",
+                     "minute", "second", "microsecond"):
+            value = getattr(res, attr)
+            if value is not None:
+                repl[attr] = value
+
+        if 'day' not in repl:
+            # If the default day exceeds the last day of the month, fall back
+            # to the end of the month.
+            cyear = default.year if res.year is None else res.year
+            cmonth = default.month if res.month is None else res.month
+            cday = default.day if res.day is None else res.day
+
+            if cday > monthrange(cyear, cmonth)[1]:
+                repl['day'] = monthrange(cyear, cmonth)[1]
+
+        naive = default.replace(**repl)
+
+        if res.weekday is not None and not res.day:
+            naive = naive + relativedelta.relativedelta(weekday=res.weekday)
+
+        return naive
+
+    def _assign_tzname(self, dt, tzname):
+        if dt.tzname() != tzname:
+            new_dt = tz.enfold(dt, fold=1)
+            if new_dt.tzname() == tzname:
+                return new_dt
+
+        return dt
+
+    def _recombine_skipped(self, tokens, skipped_idxs):
+        """
+        >>> tokens = ["foo", " ", "bar", " ", "19June2000", "baz"]
+        >>> skipped_idxs = [0, 1, 2, 5]
+        >>> _recombine_skipped(tokens, skipped_idxs)
+        ["foo bar", "baz"]
+        """
+        skipped_tokens = []
+        for i, idx in enumerate(sorted(skipped_idxs)):
+            if i > 0 and idx - 1 == skipped_idxs[i - 1]:
+                skipped_tokens[-1] = skipped_tokens[-1] + tokens[idx]
+            else:
+                skipped_tokens.append(tokens[idx])
+
+        return skipped_tokens
+
+
+DEFAULTPARSER = parser()
+
+
+def parse(timestr, parserinfo=None, **kwargs):
+    """
+
+    Parse a string in one of the supported formats, using the
+    ``parserinfo`` parameters.
+
+    :param timestr:
+        A string containing a date/time stamp.
+
+    :param parserinfo:
+        A :class:`parserinfo` object containing parameters for the parser.
+        If ``None``, the default arguments to the :class:`parserinfo`
+        constructor are used.
+
+    The ``**kwargs`` parameter takes the following keyword arguments:
+
+    :param default:
+        The default datetime object, if this is a datetime object and not
+        ``None``, elements specified in ``timestr`` replace elements in the
+        default object.
+
+    :param ignoretz:
+        If set ``True``, time zones in parsed strings are ignored and a naive
+        :class:`datetime` object is returned.
+
+    :param tzinfos:
+        Additional time zone names / aliases which may be present in the
+        string. This argument maps time zone names (and optionally offsets
+        from those time zones) to time zones. This parameter can be a
+        dictionary with timezone aliases mapping time zone names to time
+        zones or a function taking two parameters (``tzname`` and
+        ``tzoffset``) and returning a time zone.
+
+        The timezones to which the names are mapped can be an integer
+        offset from UTC in seconds or a :class:`tzinfo` object.
+
+        .. doctest::
+           :options: +NORMALIZE_WHITESPACE
+
+            >>> from dateutil.parser import parse
+            >>> from dateutil.tz import gettz
+            >>> tzinfos = {"BRST": -7200, "CST": gettz("America/Chicago")}
+            >>> parse("2012-01-19 17:21:00 BRST", tzinfos=tzinfos)
+            datetime.datetime(2012, 1, 19, 17, 21, tzinfo=tzoffset(u'BRST', -7200))
+            >>> parse("2012-01-19 17:21:00 CST", tzinfos=tzinfos)
+            datetime.datetime(2012, 1, 19, 17, 21,
+                              tzinfo=tzfile('/usr/share/zoneinfo/America/Chicago'))
+
+        This parameter is ignored if ``ignoretz`` is set.
+
+    :param dayfirst:
+        Whether to interpret the first value in an ambiguous 3-integer date
+        (e.g. 01/05/09) as the day (``True``) or month (``False``). If
+        ``yearfirst`` is set to ``True``, this distinguishes between YDM and
+        YMD. If set to ``None``, this value is retrieved from the current
+        :class:`parserinfo` object (which itself defaults to ``False``).
+
+    :param yearfirst:
+        Whether to interpret the first value in an ambiguous 3-integer date
+        (e.g. 01/05/09) as the year. If ``True``, the first number is taken to
+        be the year, otherwise the last number is taken to be the year. If
+        this is set to ``None``, the value is retrieved from the current
+        :class:`parserinfo` object (which itself defaults to ``False``).
+
+    :param fuzzy:
+        Whether to allow fuzzy parsing, allowing for string like "Today is
+        January 1, 2047 at 8:21:00AM".
+
+    :param fuzzy_with_tokens:
+        If ``True``, ``fuzzy`` is automatically set to True, and the parser
+        will return a tuple where the first element is the parsed
+        :class:`datetime.datetime` datetimestamp and the second element is
+        a tuple containing the portions of the string which were ignored:
+
+        .. doctest::
+
+            >>> from dateutil.parser import parse
+            >>> parse("Today is January 1, 2047 at 8:21:00AM", fuzzy_with_tokens=True)
+            (datetime.datetime(2047, 1, 1, 8, 21), (u'Today is ', u' ', u'at '))
+
+    :return:
+        Returns a :class:`datetime.datetime` object or, if the
+        ``fuzzy_with_tokens`` option is ``True``, returns a tuple, the
+        first element being a :class:`datetime.datetime` object, the second
+        a tuple containing the fuzzy tokens.
+
+    :raises ParserError:
+        Raised for invalid or unknown string formats, if the provided
+        :class:`tzinfo` is not in a valid format, or if an invalid date would
+        be created.
+
+    :raises OverflowError:
+        Raised if the parsed date exceeds the largest valid C integer on
+        your system.
+    """
+    if parserinfo:
+        return parser(parserinfo).parse(timestr, **kwargs)
+    else:
+        return DEFAULTPARSER.parse(timestr, **kwargs)
+
+
+class _tzparser(object):
+
+    class _result(_resultbase):
+
+        __slots__ = ["stdabbr", "stdoffset", "dstabbr", "dstoffset",
+                     "start", "end"]
+
+        class _attr(_resultbase):
+            __slots__ = ["month", "week", "weekday",
+                         "yday", "jyday", "day", "time"]
+
+        def __repr__(self):
+            return self._repr("")
+
+        def __init__(self):
+            _resultbase.__init__(self)
+            self.start = self._attr()
+            self.end = self._attr()
+
+    def parse(self, tzstr):
+        res = self._result()
+        l = [x for x in re.split(r'([,:.]|[a-zA-Z]+|[0-9]+)',tzstr) if x]
+        used_idxs = list()
+        try:
+
+            len_l = len(l)
+
+            i = 0
+            while i < len_l:
+                # BRST+3[BRDT[+2]]
+                j = i
+                while j < len_l and not [x for x in l[j]
+                                         if x in "0123456789:,-+"]:
+                    j += 1
+                if j != i:
+                    if not res.stdabbr:
+                        offattr = "stdoffset"
+                        res.stdabbr = "".join(l[i:j])
+                    else:
+                        offattr = "dstoffset"
+                        res.dstabbr = "".join(l[i:j])
+
+                    for ii in range(j):
+                        used_idxs.append(ii)
+                    i = j
+                    if (i < len_l and (l[i] in ('+', '-') or l[i][0] in
+                                       "0123456789")):
+                        if l[i] in ('+', '-'):
+                            # Yes, that's right.  See the TZ variable
+                            # documentation.
+                            signal = (1, -1)[l[i] == '+']
+                            used_idxs.append(i)
+                            i += 1
+                        else:
+                            signal = -1
+                        len_li = len(l[i])
+                        if len_li == 4:
+                            # -0300
+                            setattr(res, offattr, (int(l[i][:2]) * 3600 +
+                                                   int(l[i][2:]) * 60) * signal)
+                        elif i + 1 < len_l and l[i + 1] == ':':
+                            # -03:00
+                            setattr(res, offattr,
+                                    (int(l[i]) * 3600 +
+                                     int(l[i + 2]) * 60) * signal)
+                            used_idxs.append(i)
+                            i += 2
+                        elif len_li <= 2:
+                            # -[0]3
+                            setattr(res, offattr,
+                                    int(l[i][:2]) * 3600 * signal)
+                        else:
+                            return None
+                        used_idxs.append(i)
+                        i += 1
+                    if res.dstabbr:
+                        break
+                else:
+                    break
+
+
+            if i < len_l:
+                for j in range(i, len_l):
+                    if l[j] == ';':
+                        l[j] = ','
+
+                assert l[i] == ','
+
+                i += 1
+
+            if i >= len_l:
+                pass
+            elif (8 <= l.count(',') <= 9 and
+                  not [y for x in l[i:] if x != ','
+                       for y in x if y not in "0123456789+-"]):
+                # GMT0BST,3,0,30,3600,10,0,26,7200[,3600]
+                for x in (res.start, res.end):
+                    x.month = int(l[i])
+                    used_idxs.append(i)
+                    i += 2
+                    if l[i] == '-':
+                        value = int(l[i + 1]) * -1
+                        used_idxs.append(i)
+                        i += 1
+                    else:
+                        value = int(l[i])
+                    used_idxs.append(i)
+                    i += 2
+                    if value:
+                        x.week = value
+                        x.weekday = (int(l[i]) - 1) % 7
+                    else:
+                        x.day = int(l[i])
+                    used_idxs.append(i)
+                    i += 2
+                    x.time = int(l[i])
+                    used_idxs.append(i)
+                    i += 2
+                if i < len_l:
+                    if l[i] in ('-', '+'):
+                        signal = (-1, 1)[l[i] == "+"]
+                        used_idxs.append(i)
+                        i += 1
+                    else:
+                        signal = 1
+                    used_idxs.append(i)
+                    res.dstoffset = (res.stdoffset + int(l[i]) * signal)
+
+                # This was a made-up format that is not in normal use
+                warn(('Parsed time zone "%s"' % tzstr) +
+                     'is in a non-standard dateutil-specific format, which ' +
+                     'is now deprecated; support for parsing this format ' +
+                     'will be removed in future versions. It is recommended ' +
+                     'that you switch to a standard format like the GNU ' +
+                     'TZ variable format.', tz.DeprecatedTzFormatWarning)
+            elif (l.count(',') == 2 and l[i:].count('/') <= 2 and
+                  not [y for x in l[i:] if x not in (',', '/', 'J', 'M',
+                                                     '.', '-', ':')
+                       for y in x if y not in "0123456789"]):
+                for x in (res.start, res.end):
+                    if l[i] == 'J':
+                        # non-leap year day (1 based)
+                        used_idxs.append(i)
+                        i += 1
+                        x.jyday = int(l[i])
+                    elif l[i] == 'M':
+                        # month[-.]week[-.]weekday
+                        used_idxs.append(i)
+                        i += 1
+                        x.month = int(l[i])
+                        used_idxs.append(i)
+                        i += 1
+                        assert l[i] in ('-', '.')
+                        used_idxs.append(i)
+                        i += 1
+                        x.week = int(l[i])
+                        if x.week == 5:
+                            x.week = -1
+                        used_idxs.append(i)
+                        i += 1
+                        assert l[i] in ('-', '.')
+                        used_idxs.append(i)
+                        i += 1
+                        x.weekday = (int(l[i]) - 1) % 7
+                    else:
+                        # year day (zero based)
+                        x.yday = int(l[i]) + 1
+
+                    used_idxs.append(i)
+                    i += 1
+
+                    if i < len_l and l[i] == '/':
+                        used_idxs.append(i)
+                        i += 1
+                        # start time
+                        len_li = len(l[i])
+                        if len_li == 4:
+                            # -0300
+                            x.time = (int(l[i][:2]) * 3600 +
+                                      int(l[i][2:]) * 60)
+                        elif i + 1 < len_l and l[i + 1] == ':':
+                            # -03:00
+                            x.time = int(l[i]) * 3600 + int(l[i + 2]) * 60
+                            used_idxs.append(i)
+                            i += 2
+                            if i + 1 < len_l and l[i + 1] == ':':
+                                used_idxs.append(i)
+                                i += 2
+                                x.time += int(l[i])
+                        elif len_li <= 2:
+                            # -[0]3
+                            x.time = (int(l[i][:2]) * 3600)
+                        else:
+                            return None
+                        used_idxs.append(i)
+                        i += 1
+
+                    assert i == len_l or l[i] == ','
+
+                    i += 1
+
+                assert i >= len_l
+
+        except (IndexError, ValueError, AssertionError):
+            return None
+
+        unused_idxs = set(range(len_l)).difference(used_idxs)
+        res.any_unused_tokens = not {l[n] for n in unused_idxs}.issubset({",",":"})
+        return res
+
+
+DEFAULTTZPARSER = _tzparser()
+
+
+def _parsetz(tzstr):
+    return DEFAULTTZPARSER.parse(tzstr)
+
+
+class ParserError(ValueError):
+    """Exception subclass used for any failure to parse a datetime string.
+
+    This is a subclass of :py:exc:`ValueError`, and should be raised any time
+    earlier versions of ``dateutil`` would have raised ``ValueError``.
+
+    .. versionadded:: 2.8.1
+    """
+    def __str__(self):
+        try:
+            return self.args[0] % self.args[1:]
+        except (TypeError, IndexError):
+            return super(ParserError, self).__str__()
+
+    def __repr__(self):
+        args = ", ".join("'%s'" % arg for arg in self.args)
+        return "%s(%s)" % (self.__class__.__name__, args)
+
+
+class UnknownTimezoneWarning(RuntimeWarning):
+    """Raised when the parser finds a timezone it cannot parse into a tzinfo.
+
+    .. versionadded:: 2.7.0
+    """
+# vim:ts=4:sw=4:et

venv/lib/python3.10/site-packages/dateutil/parser/isoparser.py

@@ -0,0 +1,416 @@
+# -*- coding: utf-8 -*-
+"""
+This module offers a parser for ISO-8601 strings
+
+It is intended to support all valid date, time and datetime formats per the
+ISO-8601 specification.
+
+..versionadded:: 2.7.0
+"""
+from datetime import datetime, timedelta, time, date
+import calendar
+from dateutil import tz
+
+from functools import wraps
+
+import re
+import six
+
+__all__ = ["isoparse", "isoparser"]
+
+
+def _takes_ascii(f):
+    @wraps(f)
+    def func(self, str_in, *args, **kwargs):
+        # If it's a stream, read the whole thing
+        str_in = getattr(str_in, 'read', lambda: str_in)()
+
+        # If it's unicode, turn it into bytes, since ISO-8601 only covers ASCII
+        if isinstance(str_in, six.text_type):
+            # ASCII is the same in UTF-8
+            try:
+                str_in = str_in.encode('ascii')
+            except UnicodeEncodeError as e:
+                msg = 'ISO-8601 strings should contain only ASCII characters'
+                six.raise_from(ValueError(msg), e)
+
+        return f(self, str_in, *args, **kwargs)
+
+    return func
+
+
+class isoparser(object):
+    def __init__(self, sep=None):
+        """
+        :param sep:
+            A single character that separates date and time portions. If
+            ``None``, the parser will accept any single character.
+            For strict ISO-8601 adherence, pass ``'T'``.
+        """
+        if sep is not None:
+            if (len(sep) != 1 or ord(sep) >= 128 or sep in '0123456789'):
+                raise ValueError('Separator must be a single, non-numeric ' +
+                                 'ASCII character')
+
+            sep = sep.encode('ascii')
+
+        self._sep = sep
+
+    @_takes_ascii
+    def isoparse(self, dt_str):
+        """
+        Parse an ISO-8601 datetime string into a :class:`datetime.datetime`.
+
+        An ISO-8601 datetime string consists of a date portion, followed
+        optionally by a time portion - the date and time portions are separated
+        by a single character separator, which is ``T`` in the official
+        standard. Incomplete date formats (such as ``YYYY-MM``) may *not* be
+        combined with a time portion.
+
+        Supported date formats are:
+
+        Common:
+
+        - ``YYYY``
+        - ``YYYY-MM``
+        - ``YYYY-MM-DD`` or ``YYYYMMDD``
+
+        Uncommon:
+
+        - ``YYYY-Www`` or ``YYYYWww`` - ISO week (day defaults to 0)
+        - ``YYYY-Www-D`` or ``YYYYWwwD`` - ISO week and day
+
+        The ISO week and day numbering follows the same logic as
+        :func:`datetime.date.isocalendar`.
+
+        Supported time formats are:
+
+        - ``hh``
+        - ``hh:mm`` or ``hhmm``
+        - ``hh:mm:ss`` or ``hhmmss``
+        - ``hh:mm:ss.ssssss`` (Up to 6 sub-second digits)
+
+        Midnight is a special case for `hh`, as the standard supports both
+        00:00 and 24:00 as a representation. The decimal separator can be
+        either a dot or a comma.
+
+
+        .. caution::
+
+            Support for fractional components other than seconds is part of the
+            ISO-8601 standard, but is not currently implemented in this parser.
+
+        Supported time zone offset formats are:
+
+        - `Z` (UTC)
+        - `±HH:MM`
+        - `±HHMM`
+        - `±HH`
+
+        Offsets will be represented as :class:`dateutil.tz.tzoffset` objects,
+        with the exception of UTC, which will be represented as
+        :class:`dateutil.tz.tzutc`. Time zone offsets equivalent to UTC (such
+        as `+00:00`) will also be represented as :class:`dateutil.tz.tzutc`.
+
+        :param dt_str:
+            A string or stream containing only an ISO-8601 datetime string
+
+        :return:
+            Returns a :class:`datetime.datetime` representing the string.
+            Unspecified components default to their lowest value.
+
+        .. warning::
+
+            As of version 2.7.0, the strictness of the parser should not be
+            considered a stable part of the contract. Any valid ISO-8601 string
+            that parses correctly with the default settings will continue to
+            parse correctly in future versions, but invalid strings that
+            currently fail (e.g. ``2017-01-01T00:00+00:00:00``) are not
+            guaranteed to continue failing in future versions if they encode
+            a valid date.
+
+        .. versionadded:: 2.7.0
+        """
+        components, pos = self._parse_isodate(dt_str)
+
+        if len(dt_str) > pos:
+            if self._sep is None or dt_str[pos:pos + 1] == self._sep:
+                components += self._parse_isotime(dt_str[pos + 1:])
+            else:
+                raise ValueError('String contains unknown ISO components')
+
+        if len(components) > 3 and components[3] == 24:
+            components[3] = 0
+            return datetime(*components) + timedelta(days=1)
+
+        return datetime(*components)
+
+    @_takes_ascii
+    def parse_isodate(self, datestr):
+        """
+        Parse the date portion of an ISO string.
+
+        :param datestr:
+            The string portion of an ISO string, without a separator
+
+        :return:
+            Returns a :class:`datetime.date` object
+        """
+        components, pos = self._parse_isodate(datestr)
+        if pos < len(datestr):
+            raise ValueError('String contains unknown ISO ' +
+                             'components: {!r}'.format(datestr.decode('ascii')))
+        return date(*components)
+
+    @_takes_ascii
+    def parse_isotime(self, timestr):
+        """
+        Parse the time portion of an ISO string.
+
+        :param timestr:
+            The time portion of an ISO string, without a separator
+
+        :return:
+            Returns a :class:`datetime.time` object
+        """
+        components = self._parse_isotime(timestr)
+        if components[0] == 24:
+            components[0] = 0
+        return time(*components)
+
+    @_takes_ascii
+    def parse_tzstr(self, tzstr, zero_as_utc=True):
+        """
+        Parse a valid ISO time zone string.
+
+        See :func:`isoparser.isoparse` for details on supported formats.
+
+        :param tzstr:
+            A string representing an ISO time zone offset
+
+        :param zero_as_utc:
+            Whether to return :class:`dateutil.tz.tzutc` for zero-offset zones
+
+        :return:
+            Returns :class:`dateutil.tz.tzoffset` for offsets and
+            :class:`dateutil.tz.tzutc` for ``Z`` and (if ``zero_as_utc`` is
+            specified) offsets equivalent to UTC.
+        """
+        return self._parse_tzstr(tzstr, zero_as_utc=zero_as_utc)
+
+    # Constants
+    _DATE_SEP = b'-'
+    _TIME_SEP = b':'
+    _FRACTION_REGEX = re.compile(b'[\\.,]([0-9]+)')
+
+    def _parse_isodate(self, dt_str):
+        try:
+            return self._parse_isodate_common(dt_str)
+        except ValueError:
+            return self._parse_isodate_uncommon(dt_str)
+
+    def _parse_isodate_common(self, dt_str):
+        len_str = len(dt_str)
+        components = [1, 1, 1]
+
+        if len_str < 4:
+            raise ValueError('ISO string too short')
+
+        # Year
+        components[0] = int(dt_str[0:4])
+        pos = 4
+        if pos >= len_str:
+            return components, pos
+
+        has_sep = dt_str[pos:pos + 1] == self._DATE_SEP
+        if has_sep:
+            pos += 1
+
+        # Month
+        if len_str - pos < 2:
+            raise ValueError('Invalid common month')
+
+        components[1] = int(dt_str[pos:pos + 2])
+        pos += 2
+
+        if pos >= len_str:
+            if has_sep:
+                return components, pos
+            else:
+                raise ValueError('Invalid ISO format')
+
+        if has_sep:
+            if dt_str[pos:pos + 1] != self._DATE_SEP:
+                raise ValueError('Invalid separator in ISO string')
+            pos += 1
+
+        # Day
+        if len_str - pos < 2:
+            raise ValueError('Invalid common day')
+        components[2] = int(dt_str[pos:pos + 2])
+        return components, pos + 2
+
+    def _parse_isodate_uncommon(self, dt_str):
+        if len(dt_str) < 4:
+            raise ValueError('ISO string too short')
+
+        # All ISO formats start with the year
+        year = int(dt_str[0:4])
+
+        has_sep = dt_str[4:5] == self._DATE_SEP
+
+        pos = 4 + has_sep       # Skip '-' if it's there
+        if dt_str[pos:pos + 1] == b'W':
+            # YYYY-?Www-?D?
+            pos += 1
+            weekno = int(dt_str[pos:pos + 2])
+            pos += 2
+
+            dayno = 1
+            if len(dt_str) > pos:
+                if (dt_str[pos:pos + 1] == self._DATE_SEP) != has_sep:
+                    raise ValueError('Inconsistent use of dash separator')
+
+                pos += has_sep
+
+                dayno = int(dt_str[pos:pos + 1])
+                pos += 1
+
+            base_date = self._calculate_weekdate(year, weekno, dayno)
+        else:
+            # YYYYDDD or YYYY-DDD
+            if len(dt_str) - pos < 3:
+                raise ValueError('Invalid ordinal day')
+
+            ordinal_day = int(dt_str[pos:pos + 3])
+            pos += 3
+
+            if ordinal_day < 1 or ordinal_day > (365 + calendar.isleap(year)):
+                raise ValueError('Invalid ordinal day' +
+                                 ' {} for year {}'.format(ordinal_day, year))
+
+            base_date = date(year, 1, 1) + timedelta(days=ordinal_day - 1)
+
+        components = [base_date.year, base_date.month, base_date.day]
+        return components, pos
+
+    def _calculate_weekdate(self, year, week, day):
+        """
+        Calculate the day of corresponding to the ISO year-week-day calendar.
+
+        This function is effectively the inverse of
+        :func:`datetime.date.isocalendar`.
+
+        :param year:
+            The year in the ISO calendar
+
+        :param week:
+            The week in the ISO calendar - range is [1, 53]
+
+        :param day:
+            The day in the ISO calendar - range is [1 (MON), 7 (SUN)]
+
+        :return:
+            Returns a :class:`datetime.date`
+        """
+        if not 0 < week < 54:
+            raise ValueError('Invalid week: {}'.format(week))
+
+        if not 0 < day < 8:     # Range is 1-7
+            raise ValueError('Invalid weekday: {}'.format(day))
+
+        # Get week 1 for the specific year:
+        jan_4 = date(year, 1, 4)   # Week 1 always has January 4th in it
+        week_1 = jan_4 - timedelta(days=jan_4.isocalendar()[2] - 1)
+
+        # Now add the specific number of weeks and days to get what we want
+        week_offset = (week - 1) * 7 + (day - 1)
+        return week_1 + timedelta(days=week_offset)
+
+    def _parse_isotime(self, timestr):
+        len_str = len(timestr)
+        components = [0, 0, 0, 0, None]
+        pos = 0
+        comp = -1
+
+        if len_str < 2:
+            raise ValueError('ISO time too short')
+
+        has_sep = False
+
+        while pos < len_str and comp < 5:
+            comp += 1
+
+            if timestr[pos:pos + 1] in b'-+Zz':
+                # Detect time zone boundary
+                components[-1] = self._parse_tzstr(timestr[pos:])
+                pos = len_str
+                break
+
+            if comp == 1 and timestr[pos:pos+1] == self._TIME_SEP:
+                has_sep = True
+                pos += 1
+            elif comp == 2 and has_sep:
+                if timestr[pos:pos+1] != self._TIME_SEP:
+                    raise ValueError('Inconsistent use of colon separator')
+                pos += 1
+
+            if comp < 3:
+                # Hour, minute, second
+                components[comp] = int(timestr[pos:pos + 2])
+                pos += 2
+
+            if comp == 3:
+                # Fraction of a second
+                frac = self._FRACTION_REGEX.match(timestr[pos:])
+                if not frac:
+                    continue
+
+                us_str = frac.group(1)[:6]  # Truncate to microseconds
+                components[comp] = int(us_str) * 10**(6 - len(us_str))
+                pos += len(frac.group())
+
+        if pos < len_str:
+            raise ValueError('Unused components in ISO string')
+
+        if components[0] == 24:
+            # Standard supports 00:00 and 24:00 as representations of midnight
+            if any(component != 0 for component in components[1:4]):
+                raise ValueError('Hour may only be 24 at 24:00:00.000')
+
+        return components
+
+    def _parse_tzstr(self, tzstr, zero_as_utc=True):
+        if tzstr == b'Z' or tzstr == b'z':
+            return tz.UTC
+
+        if len(tzstr) not in {3, 5, 6}:
+            raise ValueError('Time zone offset must be 1, 3, 5 or 6 characters')
+
+        if tzstr[0:1] == b'-':
+            mult = -1
+        elif tzstr[0:1] == b'+':
+            mult = 1
+        else:
+            raise ValueError('Time zone offset requires sign')
+
+        hours = int(tzstr[1:3])
+        if len(tzstr) == 3:
+            minutes = 0
+        else:
+            minutes = int(tzstr[(4 if tzstr[3:4] == self._TIME_SEP else 3):])
+
+        if zero_as_utc and hours == 0 and minutes == 0:
+            return tz.UTC
+        else:
+            if minutes > 59:
+                raise ValueError('Invalid minutes in time zone offset')
+
+            if hours > 23:
+                raise ValueError('Invalid hours in time zone offset')
+
+            return tz.tzoffset(None, mult * (hours * 60 + minutes) * 60)
+
+
+DEFAULT_ISOPARSER = isoparser()
+isoparse = DEFAULT_ISOPARSER.isoparse

venv/lib/python3.10/site-packages/dateutil/rrule.py

@@ -0,0 +1,1737 @@
+# -*- coding: utf-8 -*-
+"""
+The rrule module offers a small, complete, and very fast, implementation of
+the recurrence rules documented in the
+`iCalendar RFC <https://tools.ietf.org/html/rfc5545>`_,
+including support for caching of results.
+"""
+import calendar
+import datetime
+import heapq
+import itertools
+import re
+import sys
+from functools import wraps
+# For warning about deprecation of until and count
+from warnings import warn
+
+from six import advance_iterator, integer_types
+
+from six.moves import _thread, range
+
+from ._common import weekday as weekdaybase
+
+try:
+    from math import gcd
+except ImportError:
+    from fractions import gcd
+
+__all__ = ["rrule", "rruleset", "rrulestr",
+           "YEARLY", "MONTHLY", "WEEKLY", "DAILY",
+           "HOURLY", "MINUTELY", "SECONDLY",
+           "MO", "TU", "WE", "TH", "FR", "SA", "SU"]
+
+# Every mask is 7 days longer to handle cross-year weekly periods.
+M366MASK = tuple([1]*31+[2]*29+[3]*31+[4]*30+[5]*31+[6]*30 +
+                 [7]*31+[8]*31+[9]*30+[10]*31+[11]*30+[12]*31+[1]*7)
+M365MASK = list(M366MASK)
+M29, M30, M31 = list(range(1, 30)), list(range(1, 31)), list(range(1, 32))
+MDAY366MASK = tuple(M31+M29+M31+M30+M31+M30+M31+M31+M30+M31+M30+M31+M31[:7])
+MDAY365MASK = list(MDAY366MASK)
+M29, M30, M31 = list(range(-29, 0)), list(range(-30, 0)), list(range(-31, 0))
+NMDAY366MASK = tuple(M31+M29+M31+M30+M31+M30+M31+M31+M30+M31+M30+M31+M31[:7])
+NMDAY365MASK = list(NMDAY366MASK)
+M366RANGE = (0, 31, 60, 91, 121, 152, 182, 213, 244, 274, 305, 335, 366)
+M365RANGE = (0, 31, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334, 365)
+WDAYMASK = [0, 1, 2, 3, 4, 5, 6]*55
+del M29, M30, M31, M365MASK[59], MDAY365MASK[59], NMDAY365MASK[31]
+MDAY365MASK = tuple(MDAY365MASK)
+M365MASK = tuple(M365MASK)
+
+FREQNAMES = ['YEARLY', 'MONTHLY', 'WEEKLY', 'DAILY', 'HOURLY', 'MINUTELY', 'SECONDLY']
+
+(YEARLY,
+ MONTHLY,
+ WEEKLY,
+ DAILY,
+ HOURLY,
+ MINUTELY,
+ SECONDLY) = list(range(7))
+
+# Imported on demand.
+easter = None
+parser = None
+
+
+class weekday(weekdaybase):
+    """
+    This version of weekday does not allow n = 0.
+    """
+    def __init__(self, wkday, n=None):
+        if n == 0:
+            raise ValueError("Can't create weekday with n==0")
+
+        super(weekday, self).__init__(wkday, n)
+
+
+MO, TU, WE, TH, FR, SA, SU = weekdays = tuple(weekday(x) for x in range(7))
+
+
+def _invalidates_cache(f):
+    """
+    Decorator for rruleset methods which may invalidate the
+    cached length.
+    """
+    @wraps(f)
+    def inner_func(self, *args, **kwargs):
+        rv = f(self, *args, **kwargs)
+        self._invalidate_cache()
+        return rv
+
+    return inner_func
+
+
+class rrulebase(object):
+    def __init__(self, cache=False):
+        if cache:
+            self._cache = []
+            self._cache_lock = _thread.allocate_lock()
+            self._invalidate_cache()
+        else:
+            self._cache = None
+            self._cache_complete = False
+            self._len = None
+
+    def __iter__(self):
+        if self._cache_complete:
+            return iter(self._cache)
+        elif self._cache is None:
+            return self._iter()
+        else:
+            return self._iter_cached()
+
+    def _invalidate_cache(self):
+        if self._cache is not None:
+            self._cache = []
+            self._cache_complete = False
+            self._cache_gen = self._iter()
+
+            if self._cache_lock.locked():
+                self._cache_lock.release()
+
+        self._len = None
+
+    def _iter_cached(self):
+        i = 0
+        gen = self._cache_gen
+        cache = self._cache
+        acquire = self._cache_lock.acquire
+        release = self._cache_lock.release
+        while gen:
+            if i == len(cache):
+                acquire()
+                if self._cache_complete:
+                    break
+                try:
+                    for j in range(10):
+                        cache.append(advance_iterator(gen))
+                except StopIteration:
+                    self._cache_gen = gen = None
+                    self._cache_complete = True
+                    break
+                release()
+            yield cache[i]
+            i += 1
+        while i < self._len:
+            yield cache[i]
+            i += 1
+
+    def __getitem__(self, item):
+        if self._cache_complete:
+            return self._cache[item]
+        elif isinstance(item, slice):
+            if item.step and item.step < 0:
+                return list(iter(self))[item]
+            else:
+                return list(itertools.islice(self,
+                                             item.start or 0,
+                                             item.stop or sys.maxsize,
+                                             item.step or 1))
+        elif item >= 0:
+            gen = iter(self)
+            try:
+                for i in range(item+1):
+                    res = advance_iterator(gen)
+            except StopIteration:
+                raise IndexError
+            return res
+        else:
+            return list(iter(self))[item]
+
+    def __contains__(self, item):
+        if self._cache_complete:
+            return item in self._cache
+        else:
+            for i in self:
+                if i == item:
+                    return True
+                elif i > item:
+                    return False
+        return False
+
+    # __len__() introduces a large performance penalty.
+    def count(self):
+        """ Returns the number of recurrences in this set. It will have go
+            through the whole recurrence, if this hasn't been done before. """
+        if self._len is None:
+            for x in self:
+                pass
+        return self._len
+
+    def before(self, dt, inc=False):
+        """ Returns the last recurrence before the given datetime instance. The
+            inc keyword defines what happens if dt is an occurrence. With
+            inc=True, if dt itself is an occurrence, it will be returned. """
+        if self._cache_complete:
+            gen = self._cache
+        else:
+            gen = self
+        last = None
+        if inc:
+            for i in gen:
+                if i > dt:
+                    break
+                last = i
+        else:
+            for i in gen:
+                if i >= dt:
+                    break
+                last = i
+        return last
+
+    def after(self, dt, inc=False):
+        """ Returns the first recurrence after the given datetime instance. The
+            inc keyword defines what happens if dt is an occurrence. With
+            inc=True, if dt itself is an occurrence, it will be returned.  """
+        if self._cache_complete:
+            gen = self._cache
+        else:
+            gen = self
+        if inc:
+            for i in gen:
+                if i >= dt:
+                    return i
+        else:
+            for i in gen:
+                if i > dt:
+                    return i
+        return None
+
+    def xafter(self, dt, count=None, inc=False):
+        """
+        Generator which yields up to `count` recurrences after the given
+        datetime instance, equivalent to `after`.
+
+        :param dt:
+            The datetime at which to start generating recurrences.
+
+        :param count:
+            The maximum number of recurrences to generate. If `None` (default),
+            dates are generated until the recurrence rule is exhausted.
+
+        :param inc:
+            If `dt` is an instance of the rule and `inc` is `True`, it is
+            included in the output.
+
+        :yields: Yields a sequence of `datetime` objects.
+        """
+
+        if self._cache_complete:
+            gen = self._cache
+        else:
+            gen = self
+
+        # Select the comparison function
+        if inc:
+            comp = lambda dc, dtc: dc >= dtc
+        else:
+            comp = lambda dc, dtc: dc > dtc
+
+        # Generate dates
+        n = 0
+        for d in gen:
+            if comp(d, dt):
+                if count is not None:
+                    n += 1
+                    if n > count:
+                        break
+
+                yield d
+
+    def between(self, after, before, inc=False, count=1):
+        """ Returns all the occurrences of the rrule between after and before.
+        The inc keyword defines what happens if after and/or before are
+        themselves occurrences. With inc=True, they will be included in the
+        list, if they are found in the recurrence set. """
+        if self._cache_complete:
+            gen = self._cache
+        else:
+            gen = self
+        started = False
+        l = []
+        if inc:
+            for i in gen:
+                if i > before:
+                    break
+                elif not started:
+                    if i >= after:
+                        started = True
+                        l.append(i)
+                else:
+                    l.append(i)
+        else:
+            for i in gen:
+                if i >= before:
+                    break
+                elif not started:
+                    if i > after:
+                        started = True
+                        l.append(i)
+                else:
+                    l.append(i)
+        return l
+
+
+class rrule(rrulebase):
+    """
+    That's the base of the rrule operation. It accepts all the keywords
+    defined in the RFC as its constructor parameters (except byday,
+    which was renamed to byweekday) and more. The constructor prototype is::
+
+            rrule(freq)
+
+    Where freq must be one of YEARLY, MONTHLY, WEEKLY, DAILY, HOURLY, MINUTELY,
+    or SECONDLY.
+
+    .. note::
+        Per RFC section 3.3.10, recurrence instances falling on invalid dates
+        and times are ignored rather than coerced:
+
+            Recurrence rules may generate recurrence instances with an invalid
+            date (e.g., February 30) or nonexistent local time (e.g., 1:30 AM
+            on a day where the local time is moved forward by an hour at 1:00
+            AM).  Such recurrence instances MUST be ignored and MUST NOT be
+            counted as part of the recurrence set.
+
+        This can lead to possibly surprising behavior when, for example, the
+        start date occurs at the end of the month:
+
+        >>> from dateutil.rrule import rrule, MONTHLY
+        >>> from datetime import datetime
+        >>> start_date = datetime(2014, 12, 31)
+        >>> list(rrule(freq=MONTHLY, count=4, dtstart=start_date))
+        ... # doctest: +NORMALIZE_WHITESPACE
+        [datetime.datetime(2014, 12, 31, 0, 0),
+         datetime.datetime(2015, 1, 31, 0, 0),
+         datetime.datetime(2015, 3, 31, 0, 0),
+         datetime.datetime(2015, 5, 31, 0, 0)]
+
+    Additionally, it supports the following keyword arguments:
+
+    :param dtstart:
+        The recurrence start. Besides being the base for the recurrence,
+        missing parameters in the final recurrence instances will also be
+        extracted from this date. If not given, datetime.now() will be used
+        instead.
+    :param interval:
+        The interval between each freq iteration. For example, when using
+        YEARLY, an interval of 2 means once every two years, but with HOURLY,
+        it means once every two hours. The default interval is 1.
+    :param wkst:
+        The week start day. Must be one of the MO, TU, WE constants, or an
+        integer, specifying the first day of the week. This will affect
+        recurrences based on weekly periods. The default week start is got
+        from calendar.firstweekday(), and may be modified by
+        calendar.setfirstweekday().
+    :param count:
+        If given, this determines how many occurrences will be generated.
+
+        .. note::
+            As of version 2.5.0, the use of the keyword ``until`` in conjunction
+            with ``count`` is deprecated, to make sure ``dateutil`` is fully
+            compliant with `RFC-5545 Sec. 3.3.10 <https://tools.ietf.org/
+            html/rfc5545#section-3.3.10>`_. Therefore, ``until`` and ``count``
+            **must not** occur in the same call to ``rrule``.
+    :param until:
+        If given, this must be a datetime instance specifying the upper-bound
+        limit of the recurrence. The last recurrence in the rule is the greatest
+        datetime that is less than or equal to the value specified in the
+        ``until`` parameter.
+
+        .. note::
+            As of version 2.5.0, the use of the keyword ``until`` in conjunction
+            with ``count`` is deprecated, to make sure ``dateutil`` is fully
+            compliant with `RFC-5545 Sec. 3.3.10 <https://tools.ietf.org/
+            html/rfc5545#section-3.3.10>`_. Therefore, ``until`` and ``count``
+            **must not** occur in the same call to ``rrule``.
+    :param bysetpos:
+        If given, it must be either an integer, or a sequence of integers,
+        positive or negative. Each given integer will specify an occurrence
+        number, corresponding to the nth occurrence of the rule inside the
+        frequency period. For example, a bysetpos of -1 if combined with a
+        MONTHLY frequency, and a byweekday of (MO, TU, WE, TH, FR), will
+        result in the last work day of every month.
+    :param bymonth:
+        If given, it must be either an integer, or a sequence of integers,
+        meaning the months to apply the recurrence to.
+    :param bymonthday:
+        If given, it must be either an integer, or a sequence of integers,
+        meaning the month days to apply the recurrence to.
+    :param byyearday:
+        If given, it must be either an integer, or a sequence of integers,
+        meaning the year days to apply the recurrence to.
+    :param byeaster:
+        If given, it must be either an integer, or a sequence of integers,
+        positive or negative. Each integer will define an offset from the
+        Easter Sunday. Passing the offset 0 to byeaster will yield the Easter
+        Sunday itself. This is an extension to the RFC specification.
+    :param byweekno:
+        If given, it must be either an integer, or a sequence of integers,
+        meaning the week numbers to apply the recurrence to. Week numbers
+        have the meaning described in ISO8601, that is, the first week of
+        the year is that containing at least four days of the new year.
+    :param byweekday:
+        If given, it must be either an integer (0 == MO), a sequence of
+        integers, one of the weekday constants (MO, TU, etc), or a sequence
+        of these constants. When given, these variables will define the
+        weekdays where the recurrence will be applied. It's also possible to
+        use an argument n for the weekday instances, which will mean the nth
+        occurrence of this weekday in the period. For example, with MONTHLY,
+        or with YEARLY and BYMONTH, using FR(+1) in byweekday will specify the
+        first friday of the month where the recurrence happens. Notice that in
+        the RFC documentation, this is specified as BYDAY, but was renamed to
+        avoid the ambiguity of that keyword.
+    :param byhour:
+        If given, it must be either an integer, or a sequence of integers,
+        meaning the hours to apply the recurrence to.
+    :param byminute:
+        If given, it must be either an integer, or a sequence of integers,
+        meaning the minutes to apply the recurrence to.
+    :param bysecond:
+        If given, it must be either an integer, or a sequence of integers,
+        meaning the seconds to apply the recurrence to.
+    :param cache:
+        If given, it must be a boolean value specifying to enable or disable
+        caching of results. If you will use the same rrule instance multiple
+        times, enabling caching will improve the performance considerably.
+     """
+    def __init__(self, freq, dtstart=None,
+                 interval=1, wkst=None, count=None, until=None, bysetpos=None,
+                 bymonth=None, bymonthday=None, byyearday=None, byeaster=None,
+                 byweekno=None, byweekday=None,
+                 byhour=None, byminute=None, bysecond=None,
+                 cache=False):
+        super(rrule, self).__init__(cache)
+        global easter
+        if not dtstart:
+            if until and until.tzinfo:
+                dtstart = datetime.datetime.now(tz=until.tzinfo).replace(microsecond=0)
+            else:
+                dtstart = datetime.datetime.now().replace(microsecond=0)
+        elif not isinstance(dtstart, datetime.datetime):
+            dtstart = datetime.datetime.fromordinal(dtstart.toordinal())
+        else:
+            dtstart = dtstart.replace(microsecond=0)
+        self._dtstart = dtstart
+        self._tzinfo = dtstart.tzinfo
+        self._freq = freq
+        self._interval = interval
+        self._count = count
+
+        # Cache the original byxxx rules, if they are provided, as the _byxxx
+        # attributes do not necessarily map to the inputs, and this can be
+        # a problem in generating the strings. Only store things if they've
+        # been supplied (the string retrieval will just use .get())
+        self._original_rule = {}
+
+        if until and not isinstance(until, datetime.datetime):
+            until = datetime.datetime.fromordinal(until.toordinal())
+        self._until = until
+
+        if self._dtstart and self._until:
+            if (self._dtstart.tzinfo is not None) != (self._until.tzinfo is not None):
+                # According to RFC5545 Section 3.3.10:
+                # https://tools.ietf.org/html/rfc5545#section-3.3.10
+                #
+                # > If the "DTSTART" property is specified as a date with UTC
+                # > time or a date with local time and time zone reference,
+                # > then the UNTIL rule part MUST be specified as a date with
+                # > UTC time.
+                raise ValueError(
+                    'RRULE UNTIL values must be specified in UTC when DTSTART '
+                    'is timezone-aware'
+                )
+
+        if count is not None and until:
+            warn("Using both 'count' and 'until' is inconsistent with RFC 5545"
+                 " and has been deprecated in dateutil. Future versions will "
+                 "raise an error.", DeprecationWarning)
+
+        if wkst is None:
+            self._wkst = calendar.firstweekday()
+        elif isinstance(wkst, integer_types):
+            self._wkst = wkst
+        else:
+            self._wkst = wkst.weekday
+
+        if bysetpos is None:
+            self._bysetpos = None
+        elif isinstance(bysetpos, integer_types):
+            if bysetpos == 0 or not (-366 <= bysetpos <= 366):
+                raise ValueError("bysetpos must be between 1 and 366, "
+                                 "or between -366 and -1")
+            self._bysetpos = (bysetpos,)
+        else:
+            self._bysetpos = tuple(bysetpos)
+            for pos in self._bysetpos:
+                if pos == 0 or not (-366 <= pos <= 366):
+                    raise ValueError("bysetpos must be between 1 and 366, "
+                                     "or between -366 and -1")
+
+        if self._bysetpos:
+            self._original_rule['bysetpos'] = self._bysetpos
+
+        if (byweekno is None and byyearday is None and bymonthday is None and
+                byweekday is None and byeaster is None):
+            if freq == YEARLY:
+                if bymonth is None:
+                    bymonth = dtstart.month
+                    self._original_rule['bymonth'] = None
+                bymonthday = dtstart.day
+                self._original_rule['bymonthday'] = None
+            elif freq == MONTHLY:
+                bymonthday = dtstart.day
+                self._original_rule['bymonthday'] = None
+            elif freq == WEEKLY:
+                byweekday = dtstart.weekday()
+                self._original_rule['byweekday'] = None
+
+        # bymonth
+        if bymonth is None:
+            self._bymonth = None
+        else:
+            if isinstance(bymonth, integer_types):
+                bymonth = (bymonth,)
+
+            self._bymonth = tuple(sorted(set(bymonth)))
+
+            if 'bymonth' not in self._original_rule:
+                self._original_rule['bymonth'] = self._bymonth
+
+        # byyearday
+        if byyearday is None:
+            self._byyearday = None
+        else:
+            if isinstance(byyearday, integer_types):
+                byyearday = (byyearday,)
+
+            self._byyearday = tuple(sorted(set(byyearday)))
+            self._original_rule['byyearday'] = self._byyearday
+
+        # byeaster
+        if byeaster is not None:
+            if not easter:
+                from dateutil import easter
+            if isinstance(byeaster, integer_types):
+                self._byeaster = (byeaster,)
+            else:
+                self._byeaster = tuple(sorted(byeaster))
+
+            self._original_rule['byeaster'] = self._byeaster
+        else:
+            self._byeaster = None
+
+        # bymonthday
+        if bymonthday is None:
+            self._bymonthday = ()
+            self._bynmonthday = ()
+        else:
+            if isinstance(bymonthday, integer_types):
+                bymonthday = (bymonthday,)
+
+            bymonthday = set(bymonthday)            # Ensure it's unique
+
+            self._bymonthday = tuple(sorted(x for x in bymonthday if x > 0))
+            self._bynmonthday = tuple(sorted(x for x in bymonthday if x < 0))
+
+            # Storing positive numbers first, then negative numbers
+            if 'bymonthday' not in self._original_rule:
+                self._original_rule['bymonthday'] = tuple(
+                    itertools.chain(self._bymonthday, self._bynmonthday))
+
+        # byweekno
+        if byweekno is None:
+            self._byweekno = None
+        else:
+            if isinstance(byweekno, integer_types):
+                byweekno = (byweekno,)
+
+            self._byweekno = tuple(sorted(set(byweekno)))
+
+            self._original_rule['byweekno'] = self._byweekno
+
+        # byweekday / bynweekday
+        if byweekday is None:
+            self._byweekday = None
+            self._bynweekday = None
+        else:
+            # If it's one of the valid non-sequence types, convert to a
+            # single-element sequence before the iterator that builds the
+            # byweekday set.
+            if isinstance(byweekday, integer_types) or hasattr(byweekday, "n"):
+                byweekday = (byweekday,)
+
+            self._byweekday = set()
+            self._bynweekday = set()
+            for wday in byweekday:
+                if isinstance(wday, integer_types):
+                    self._byweekday.add(wday)
+                elif not wday.n or freq > MONTHLY:
+                    self._byweekday.add(wday.weekday)
+                else:
+                    self._bynweekday.add((wday.weekday, wday.n))
+
+            if not self._byweekday:
+                self._byweekday = None
+            elif not self._bynweekday:
+                self._bynweekday = None
+
+            if self._byweekday is not None:
+                self._byweekday = tuple(sorted(self._byweekday))
+                orig_byweekday = [weekday(x) for x in self._byweekday]
+            else:
+                orig_byweekday = ()
+
+            if self._bynweekday is not None:
+                self._bynweekday = tuple(sorted(self._bynweekday))
+                orig_bynweekday = [weekday(*x) for x in self._bynweekday]
+            else:
+                orig_bynweekday = ()
+
+            if 'byweekday' not in self._original_rule:
+                self._original_rule['byweekday'] = tuple(itertools.chain(
+                    orig_byweekday, orig_bynweekday))
+
+        # byhour
+        if byhour is None:
+            if freq < HOURLY:
+                self._byhour = {dtstart.hour}
+            else:
+                self._byhour = None
+        else:
+            if isinstance(byhour, integer_types):
+                byhour = (byhour,)
+
+            if freq == HOURLY:
+                self._byhour = self.__construct_byset(start=dtstart.hour,
+                                                      byxxx=byhour,
+                                                      base=24)
+            else:
+                self._byhour = set(byhour)
+
+            self._byhour = tuple(sorted(self._byhour))
+            self._original_rule['byhour'] = self._byhour
+
+        # byminute
+        if byminute is None:
+            if freq < MINUTELY:
+                self._byminute = {dtstart.minute}
+            else:
+                self._byminute = None
+        else:
+            if isinstance(byminute, integer_types):
+                byminute = (byminute,)
+
+            if freq == MINUTELY:
+                self._byminute = self.__construct_byset(start=dtstart.minute,
+                                                        byxxx=byminute,
+                                                        base=60)
+            else:
+                self._byminute = set(byminute)
+
+            self._byminute = tuple(sorted(self._byminute))
+            self._original_rule['byminute'] = self._byminute
+
+        # bysecond
+        if bysecond is None:
+            if freq < SECONDLY:
+                self._bysecond = ((dtstart.second,))
+            else:
+                self._bysecond = None
+        else:
+            if isinstance(bysecond, integer_types):
+                bysecond = (bysecond,)
+
+            self._bysecond = set(bysecond)
+
+            if freq == SECONDLY:
+                self._bysecond = self.__construct_byset(start=dtstart.second,
+                                                        byxxx=bysecond,
+                                                        base=60)
+            else:
+                self._bysecond = set(bysecond)
+
+            self._bysecond = tuple(sorted(self._bysecond))
+            self._original_rule['bysecond'] = self._bysecond
+
+        if self._freq >= HOURLY:
+            self._timeset = None
+        else:
+            self._timeset = []
+            for hour in self._byhour:
+                for minute in self._byminute:
+                    for second in self._bysecond:
+                        self._timeset.append(
+                            datetime.time(hour, minute, second,
+                                          tzinfo=self._tzinfo))
+            self._timeset.sort()
+            self._timeset = tuple(self._timeset)
+
+    def __str__(self):
+        """
+        Output a string that would generate this RRULE if passed to rrulestr.
+        This is mostly compatible with RFC5545, except for the
+        dateutil-specific extension BYEASTER.
+        """
+
+        output = []
+        h, m, s = [None] * 3
+        if self._dtstart:
+            output.append(self._dtstart.strftime('DTSTART:%Y%m%dT%H%M%S'))
+            h, m, s = self._dtstart.timetuple()[3:6]
+
+        parts = ['FREQ=' + FREQNAMES[self._freq]]
+        if self._interval != 1:
+            parts.append('INTERVAL=' + str(self._interval))
+
+        if self._wkst:
+            parts.append('WKST=' + repr(weekday(self._wkst))[0:2])
+
+        if self._count is not None:
+            parts.append('COUNT=' + str(self._count))
+
+        if self._until:
+            parts.append(self._until.strftime('UNTIL=%Y%m%dT%H%M%S'))
+
+        if self._original_rule.get('byweekday') is not None:
+            # The str() method on weekday objects doesn't generate
+            # RFC5545-compliant strings, so we should modify that.
+            original_rule = dict(self._original_rule)
+            wday_strings = []
+            for wday in original_rule['byweekday']:
+                if wday.n:
+                    wday_strings.append('{n:+d}{wday}'.format(
+                        n=wday.n,
+                        wday=repr(wday)[0:2]))
+                else:
+                    wday_strings.append(repr(wday))
+
+            original_rule['byweekday'] = wday_strings
+        else:
+            original_rule = self._original_rule
+
+        partfmt = '{name}={vals}'
+        for name, key in [('BYSETPOS', 'bysetpos'),
+                          ('BYMONTH', 'bymonth'),
+                          ('BYMONTHDAY', 'bymonthday'),
+                          ('BYYEARDAY', 'byyearday'),
+                          ('BYWEEKNO', 'byweekno'),
+                          ('BYDAY', 'byweekday'),
+                          ('BYHOUR', 'byhour'),
+                          ('BYMINUTE', 'byminute'),
+                          ('BYSECOND', 'bysecond'),
+                          ('BYEASTER', 'byeaster')]:
+            value = original_rule.get(key)
+            if value:
+                parts.append(partfmt.format(name=name, vals=(','.join(str(v)
+                                                             for v in value))))
+
+        output.append('RRULE:' + ';'.join(parts))
+        return '\n'.join(output)
+
+    def replace(self, **kwargs):
+        """Return new rrule with same attributes except for those attributes given new
+           values by whichever keyword arguments are specified."""
+        new_kwargs = {"interval": self._interval,
+                      "count": self._count,
+                      "dtstart": self._dtstart,
+                      "freq": self._freq,
+                      "until": self._until,
+                      "wkst": self._wkst,
+                      "cache": False if self._cache is None else True }
+        new_kwargs.update(self._original_rule)
+        new_kwargs.update(kwargs)
+        return rrule(**new_kwargs)
+
+    def _iter(self):
+        year, month, day, hour, minute, second, weekday, yearday, _ = \
+            self._dtstart.timetuple()
+
+        # Some local variables to speed things up a bit
+        freq = self._freq
+        interval = self._interval
+        wkst = self._wkst
+        until = self._until
+        bymonth = self._bymonth
+        byweekno = self._byweekno
+        byyearday = self._byyearday
+        byweekday = self._byweekday
+        byeaster = self._byeaster
+        bymonthday = self._bymonthday
+        bynmonthday = self._bynmonthday
+        bysetpos = self._bysetpos
+        byhour = self._byhour
+        byminute = self._byminute
+        bysecond = self._bysecond
+
+        ii = _iterinfo(self)
+        ii.rebuild(year, month)
+
+        getdayset = {YEARLY: ii.ydayset,
+                     MONTHLY: ii.mdayset,
+                     WEEKLY: ii.wdayset,
+                     DAILY: ii.ddayset,
+                     HOURLY: ii.ddayset,
+                     MINUTELY: ii.ddayset,
+                     SECONDLY: ii.ddayset}[freq]
+
+        if freq < HOURLY:
+            timeset = self._timeset
+        else:
+            gettimeset = {HOURLY: ii.htimeset,
+                          MINUTELY: ii.mtimeset,
+                          SECONDLY: ii.stimeset}[freq]
+            if ((freq >= HOURLY and
+                 self._byhour and hour not in self._byhour) or
+                (freq >= MINUTELY and
+                 self._byminute and minute not in self._byminute) or
+                (freq >= SECONDLY and
+                 self._bysecond and second not in self._bysecond)):
+                timeset = ()
+            else:
+                timeset = gettimeset(hour, minute, second)
+
+        total = 0
+        count = self._count
+        while True:
+            # Get dayset with the right frequency
+            dayset, start, end = getdayset(year, month, day)
+
+            # Do the "hard" work ;-)
+            filtered = False
+            for i in dayset[start:end]:
+                if ((bymonth and ii.mmask[i] not in bymonth) or
+                    (byweekno and not ii.wnomask[i]) or
+                    (byweekday and ii.wdaymask[i] not in byweekday) or
+                    (ii.nwdaymask and not ii.nwdaymask[i]) or
+                    (byeaster and not ii.eastermask[i]) or
+                    ((bymonthday or bynmonthday) and
+                     ii.mdaymask[i] not in bymonthday and
+                     ii.nmdaymask[i] not in bynmonthday) or
+                    (byyearday and
+                     ((i < ii.yearlen and i+1 not in byyearday and
+                       -ii.yearlen+i not in byyearday) or
+                      (i >= ii.yearlen and i+1-ii.yearlen not in byyearday and
+                       -ii.nextyearlen+i-ii.yearlen not in byyearday)))):
+                    dayset[i] = None
+                    filtered = True
+
+            # Output results
+            if bysetpos and timeset:
+                poslist = []
+                for pos in bysetpos:
+                    if pos < 0:
+                        daypos, timepos = divmod(pos, len(timeset))
+                    else:
+                        daypos, timepos = divmod(pos-1, len(timeset))
+                    try:
+                        i = [x for x in dayset[start:end]
+                             if x is not None][daypos]
+                        time = timeset[timepos]
+                    except IndexError:
+                        pass
+                    else:
+                        date = datetime.date.fromordinal(ii.yearordinal+i)
+                        res = datetime.datetime.combine(date, time)
+                        if res not in poslist:
+                            poslist.append(res)
+                poslist.sort()
+                for res in poslist:
+                    if until and res > until:
+                        self._len = total
+                        return
+                    elif res >= self._dtstart:
+                        if count is not None:
+                            count -= 1
+                            if count < 0:
+                                self._len = total
+                                return
+                        total += 1
+                        yield res
+            else:
+                for i in dayset[start:end]:
+                    if i is not None:
+                        date = datetime.date.fromordinal(ii.yearordinal + i)
+                        for time in timeset:
+                            res = datetime.datetime.combine(date, time)
+                            if until and res > until:
+                                self._len = total
+                                return
+                            elif res >= self._dtstart:
+                                if count is not None:
+                                    count -= 1
+                                    if count < 0:
+                                        self._len = total
+                                        return
+
+                                total += 1
+                                yield res
+
+            # Handle frequency and interval
+            fixday = False
+            if freq == YEARLY:
+                year += interval
+                if year > datetime.MAXYEAR:
+                    self._len = total
+                    return
+                ii.rebuild(year, month)
+            elif freq == MONTHLY:
+                month += interval
+                if month > 12:
+                    div, mod = divmod(month, 12)
+                    month = mod
+                    year += div
+                    if month == 0:
+                        month = 12
+                        year -= 1
+                    if year > datetime.MAXYEAR:
+                        self._len = total
+                        return
+                ii.rebuild(year, month)
+            elif freq == WEEKLY:
+                if wkst > weekday:
+                    day += -(weekday+1+(6-wkst))+self._interval*7
+                else:
+                    day += -(weekday-wkst)+self._interval*7
+                weekday = wkst
+                fixday = True
+            elif freq == DAILY:
+                day += interval
+                fixday = True
+            elif freq == HOURLY:
+                if filtered:
+                    # Jump to one iteration before next day
+                    hour += ((23-hour)//interval)*interval
+
+                if byhour:
+                    ndays, hour = self.__mod_distance(value=hour,
+                                                      byxxx=self._byhour,
+                                                      base=24)
+                else:
+                    ndays, hour = divmod(hour+interval, 24)
+
+                if ndays:
+                    day += ndays
+                    fixday = True
+
+                timeset = gettimeset(hour, minute, second)
+            elif freq == MINUTELY:
+                if filtered:
+                    # Jump to one iteration before next day
+                    minute += ((1439-(hour*60+minute))//interval)*interval
+
+                valid = False
+                rep_rate = (24*60)
+                for j in range(rep_rate // gcd(interval, rep_rate)):
+                    if byminute:
+                        nhours, minute = \
+                            self.__mod_distance(value=minute,
+                                                byxxx=self._byminute,
+                                                base=60)
+                    else:
+                        nhours, minute = divmod(minute+interval, 60)
+
+                    div, hour = divmod(hour+nhours, 24)
+                    if div:
+                        day += div
+                        fixday = True
+                        filtered = False
+
+                    if not byhour or hour in byhour:
+                        valid = True
+                        break
+
+                if not valid:
+                    raise ValueError('Invalid combination of interval and ' +
+                                     'byhour resulting in empty rule.')
+
+                timeset = gettimeset(hour, minute, second)
+            elif freq == SECONDLY:
+                if filtered:
+                    # Jump to one iteration before next day
+                    second += (((86399 - (hour * 3600 + minute * 60 + second))
+                                // interval) * interval)
+
+                rep_rate = (24 * 3600)
+                valid = False
+                for j in range(0, rep_rate // gcd(interval, rep_rate)):
+                    if bysecond:
+                        nminutes, second = \
+                            self.__mod_distance(value=second,
+                                                byxxx=self._bysecond,
+                                                base=60)
+                    else:
+                        nminutes, second = divmod(second+interval, 60)
+
+                    div, minute = divmod(minute+nminutes, 60)
+                    if div:
+                        hour += div
+                        div, hour = divmod(hour, 24)
+                        if div:
+                            day += div
+                            fixday = True
+
+                    if ((not byhour or hour in byhour) and
+                            (not byminute or minute in byminute) and
+                            (not bysecond or second in bysecond)):
+                        valid = True
+                        break
+
+                if not valid:
+                    raise ValueError('Invalid combination of interval, ' +
+                                     'byhour and byminute resulting in empty' +
+                                     ' rule.')
+
+                timeset = gettimeset(hour, minute, second)
+
+            if fixday and day > 28:
+                daysinmonth = calendar.monthrange(year, month)[1]
+                if day > daysinmonth:
+                    while day > daysinmonth:
+                        day -= daysinmonth
+                        month += 1
+                        if month == 13:
+                            month = 1
+                            year += 1
+                            if year > datetime.MAXYEAR:
+                                self._len = total
+                                return
+                        daysinmonth = calendar.monthrange(year, month)[1]
+                    ii.rebuild(year, month)
+
+    def __construct_byset(self, start, byxxx, base):
+        """
+        If a `BYXXX` sequence is passed to the constructor at the same level as
+        `FREQ` (e.g. `FREQ=HOURLY,BYHOUR={2,4,7},INTERVAL=3`), there are some
+        specifications which cannot be reached given some starting conditions.
+
+        This occurs whenever the interval is not coprime with the base of a
+        given unit and the difference between the starting position and the
+        ending position is not coprime with the greatest common denominator
+        between the interval and the base. For example, with a FREQ of hourly
+        starting at 17:00 and an interval of 4, the only valid values for
+        BYHOUR would be {21, 1, 5, 9, 13, 17}, because 4 and 24 are not
+        coprime.
+
+        :param start:
+            Specifies the starting position.
+        :param byxxx:
+            An iterable containing the list of allowed values.
+        :param base:
+            The largest allowable value for the specified frequency (e.g.
+            24 hours, 60 minutes).
+
+        This does not preserve the type of the iterable, returning a set, since
+        the values should be unique and the order is irrelevant, this will
+        speed up later lookups.
+
+        In the event of an empty set, raises a :exception:`ValueError`, as this
+        results in an empty rrule.
+        """
+
+        cset = set()
+
+        # Support a single byxxx value.
+        if isinstance(byxxx, integer_types):
+            byxxx = (byxxx, )
+
+        for num in byxxx:
+            i_gcd = gcd(self._interval, base)
+            # Use divmod rather than % because we need to wrap negative nums.
+            if i_gcd == 1 or divmod(num - start, i_gcd)[1] == 0:
+                cset.add(num)
+
+        if len(cset) == 0:
+            raise ValueError("Invalid rrule byxxx generates an empty set.")
+
+        return cset
+
+    def __mod_distance(self, value, byxxx, base):
+        """
+        Calculates the next value in a sequence where the `FREQ` parameter is
+        specified along with a `BYXXX` parameter at the same "level"
+        (e.g. `HOURLY` specified with `BYHOUR`).
+
+        :param value:
+            The old value of the component.
+        :param byxxx:
+            The `BYXXX` set, which should have been generated by
+            `rrule._construct_byset`, or something else which checks that a
+            valid rule is present.
+        :param base:
+            The largest allowable value for the specified frequency (e.g.
+            24 hours, 60 minutes).
+
+        If a valid value is not found after `base` iterations (the maximum
+        number before the sequence would start to repeat), this raises a
+        :exception:`ValueError`, as no valid values were found.
+
+        This returns a tuple of `divmod(n*interval, base)`, where `n` is the
+        smallest number of `interval` repetitions until the next specified
+        value in `byxxx` is found.
+        """
+        accumulator = 0
+        for ii in range(1, base + 1):
+            # Using divmod() over % to account for negative intervals
+            div, value = divmod(value + self._interval, base)
+            accumulator += div
+            if value in byxxx:
+                return (accumulator, value)
+
+
+class _iterinfo(object):
+    __slots__ = ["rrule", "lastyear", "lastmonth",
+                 "yearlen", "nextyearlen", "yearordinal", "yearweekday",
+                 "mmask", "mrange", "mdaymask", "nmdaymask",
+                 "wdaymask", "wnomask", "nwdaymask", "eastermask"]
+
+    def __init__(self, rrule):
+        for attr in self.__slots__:
+            setattr(self, attr, None)
+        self.rrule = rrule
+
+    def rebuild(self, year, month):
+        # Every mask is 7 days longer to handle cross-year weekly periods.
+        rr = self.rrule
+        if year != self.lastyear:
+            self.yearlen = 365 + calendar.isleap(year)
+            self.nextyearlen = 365 + calendar.isleap(year + 1)
+            firstyday = datetime.date(year, 1, 1)
+            self.yearordinal = firstyday.toordinal()
+            self.yearweekday = firstyday.weekday()
+
+            wday = datetime.date(year, 1, 1).weekday()
+            if self.yearlen == 365:
+                self.mmask = M365MASK
+                self.mdaymask = MDAY365MASK
+                self.nmdaymask = NMDAY365MASK
+                self.wdaymask = WDAYMASK[wday:]
+                self.mrange = M365RANGE
+            else:
+                self.mmask = M366MASK
+                self.mdaymask = MDAY366MASK
+                self.nmdaymask = NMDAY366MASK
+                self.wdaymask = WDAYMASK[wday:]
+                self.mrange = M366RANGE
+
+            if not rr._byweekno:
+                self.wnomask = None
+            else:
+                self.wnomask = [0]*(self.yearlen+7)
+                # no1wkst = firstwkst = self.wdaymask.index(rr._wkst)
+                no1wkst = firstwkst = (7-self.yearweekday+rr._wkst) % 7
+                if no1wkst >= 4:
+                    no1wkst = 0
+                    # Number of days in the year, plus the days we got
+                    # from last year.
+                    wyearlen = self.yearlen+(self.yearweekday-rr._wkst) % 7
+                else:
+                    # Number of days in the year, minus the days we
+                    # left in last year.
+                    wyearlen = self.yearlen-no1wkst
+                div, mod = divmod(wyearlen, 7)
+                numweeks = div+mod//4
+                for n in rr._byweekno:
+                    if n < 0:
+                        n += numweeks+1
+                    if not (0 < n <= numweeks):
+                        continue
+                    if n > 1:
+                        i = no1wkst+(n-1)*7
+                        if no1wkst != firstwkst:
+                            i -= 7-firstwkst
+                    else:
+                        i = no1wkst
+                    for j in range(7):
+                        self.wnomask[i] = 1
+                        i += 1
+                        if self.wdaymask[i] == rr._wkst:
+                            break
+                if 1 in rr._byweekno:
+                    # Check week number 1 of next year as well
+                    # TODO: Check -numweeks for next year.
+                    i = no1wkst+numweeks*7
+                    if no1wkst != firstwkst:
+                        i -= 7-firstwkst
+                    if i < self.yearlen:
+                        # If week starts in next year, we
+                        # don't care about it.
+                        for j in range(7):
+                            self.wnomask[i] = 1
+                            i += 1
+                            if self.wdaymask[i] == rr._wkst:
+                                break
+                if no1wkst:
+                    # Check last week number of last year as
+                    # well. If no1wkst is 0, either the year
+                    # started on week start, or week number 1
+                    # got days from last year, so there are no
+                    # days from last year's last week number in
+                    # this year.
+                    if -1 not in rr._byweekno:
+                        lyearweekday = datetime.date(year-1, 1, 1).weekday()
+                        lno1wkst = (7-lyearweekday+rr._wkst) % 7
+                        lyearlen = 365+calendar.isleap(year-1)
+                        if lno1wkst >= 4:
+                            lno1wkst = 0
+                            lnumweeks = 52+(lyearlen +
+                                            (lyearweekday-rr._wkst) % 7) % 7//4
+                        else:
+                            lnumweeks = 52+(self.yearlen-no1wkst) % 7//4
+                    else:
+                        lnumweeks = -1
+                    if lnumweeks in rr._byweekno:
+                        for i in range(no1wkst):
+                            self.wnomask[i] = 1
+
+        if (rr._bynweekday and (month != self.lastmonth or
+                                year != self.lastyear)):
+            ranges = []
+            if rr._freq == YEARLY:
+                if rr._bymonth:
+                    for month in rr._bymonth:
+                        ranges.append(self.mrange[month-1:month+1])
+                else:
+                    ranges = [(0, self.yearlen)]
+            elif rr._freq == MONTHLY:
+                ranges = [self.mrange[month-1:month+1]]
+            if ranges:
+                # Weekly frequency won't get here, so we may not
+                # care about cross-year weekly periods.
+                self.nwdaymask = [0]*self.yearlen
+                for first, last in ranges:
+                    last -= 1
+                    for wday, n in rr._bynweekday:
+                        if n < 0:
+                            i = last+(n+1)*7
+                            i -= (self.wdaymask[i]-wday) % 7
+                        else:
+                            i = first+(n-1)*7
+                            i += (7-self.wdaymask[i]+wday) % 7
+                        if first <= i <= last:
+                            self.nwdaymask[i] = 1
+
+        if rr._byeaster:
+            self.eastermask = [0]*(self.yearlen+7)
+            eyday = easter.easter(year).toordinal()-self.yearordinal
+            for offset in rr._byeaster:
+                self.eastermask[eyday+offset] = 1
+
+        self.lastyear = year
+        self.lastmonth = month
+
+    def ydayset(self, year, month, day):
+        return list(range(self.yearlen)), 0, self.yearlen
+
+    def mdayset(self, year, month, day):
+        dset = [None]*self.yearlen
+        start, end = self.mrange[month-1:month+1]
+        for i in range(start, end):
+            dset[i] = i
+        return dset, start, end
+
+    def wdayset(self, year, month, day):
+        # We need to handle cross-year weeks here.
+        dset = [None]*(self.yearlen+7)
+        i = datetime.date(year, month, day).toordinal()-self.yearordinal
+        start = i
+        for j in range(7):
+            dset[i] = i
+            i += 1
+            # if (not (0 <= i < self.yearlen) or
+            #    self.wdaymask[i] == self.rrule._wkst):
+            # This will cross the year boundary, if necessary.
+            if self.wdaymask[i] == self.rrule._wkst:
+                break
+        return dset, start, i
+
+    def ddayset(self, year, month, day):
+        dset = [None] * self.yearlen
+        i = datetime.date(year, month, day).toordinal() - self.yearordinal
+        dset[i] = i
+        return dset, i, i + 1
+
+    def htimeset(self, hour, minute, second):
+        tset = []
+        rr = self.rrule
+        for minute in rr._byminute:
+            for second in rr._bysecond:
+                tset.append(datetime.time(hour, minute, second,
+                                          tzinfo=rr._tzinfo))
+        tset.sort()
+        return tset
+
+    def mtimeset(self, hour, minute, second):
+        tset = []
+        rr = self.rrule
+        for second in rr._bysecond:
+            tset.append(datetime.time(hour, minute, second, tzinfo=rr._tzinfo))
+        tset.sort()
+        return tset
+
+    def stimeset(self, hour, minute, second):
+        return (datetime.time(hour, minute, second,
+                tzinfo=self.rrule._tzinfo),)
+
+
+class rruleset(rrulebase):
+    """ The rruleset type allows more complex recurrence setups, mixing
+    multiple rules, dates, exclusion rules, and exclusion dates. The type
+    constructor takes the following keyword arguments:
+
+    :param cache: If True, caching of results will be enabled, improving
+                  performance of multiple queries considerably. """
+
+    class _genitem(object):
+        def __init__(self, genlist, gen):
+            try:
+                self.dt = advance_iterator(gen)
+                genlist.append(self)
+            except StopIteration:
+                pass
+            self.genlist = genlist
+            self.gen = gen
+
+        def __next__(self):
+            try:
+                self.dt = advance_iterator(self.gen)
+            except StopIteration:
+                if self.genlist[0] is self:
+                    heapq.heappop(self.genlist)
+                else:
+                    self.genlist.remove(self)
+                    heapq.heapify(self.genlist)
+
+        next = __next__
+
+        def __lt__(self, other):
+            return self.dt < other.dt
+
+        def __gt__(self, other):
+            return self.dt > other.dt
+
+        def __eq__(self, other):
+            return self.dt == other.dt
+
+        def __ne__(self, other):
+            return self.dt != other.dt
+
+    def __init__(self, cache=False):
+        super(rruleset, self).__init__(cache)
+        self._rrule = []
+        self._rdate = []
+        self._exrule = []
+        self._exdate = []
+
+    @_invalidates_cache
+    def rrule(self, rrule):
+        """ Include the given :py:class:`rrule` instance in the recurrence set
+            generation. """
+        self._rrule.append(rrule)
+
+    @_invalidates_cache
+    def rdate(self, rdate):
+        """ Include the given :py:class:`datetime` instance in the recurrence
+            set generation. """
+        self._rdate.append(rdate)
+
+    @_invalidates_cache
+    def exrule(self, exrule):
+        """ Include the given rrule instance in the recurrence set exclusion
+            list. Dates which are part of the given recurrence rules will not
+            be generated, even if some inclusive rrule or rdate matches them.
+        """
+        self._exrule.append(exrule)
+
+    @_invalidates_cache
+    def exdate(self, exdate):
+        """ Include the given datetime instance in the recurrence set
+            exclusion list. Dates included that way will not be generated,
+            even if some inclusive rrule or rdate matches them. """
+        self._exdate.append(exdate)
+
+    def _iter(self):
+        rlist = []
+        self._rdate.sort()
+        self._genitem(rlist, iter(self._rdate))
+        for gen in [iter(x) for x in self._rrule]:
+            self._genitem(rlist, gen)
+        exlist = []
+        self._exdate.sort()
+        self._genitem(exlist, iter(self._exdate))
+        for gen in [iter(x) for x in self._exrule]:
+            self._genitem(exlist, gen)
+        lastdt = None
+        total = 0
+        heapq.heapify(rlist)
+        heapq.heapify(exlist)
+        while rlist:
+            ritem = rlist[0]
+            if not lastdt or lastdt != ritem.dt:
+                while exlist and exlist[0] < ritem:
+                    exitem = exlist[0]
+                    advance_iterator(exitem)
+                    if exlist and exlist[0] is exitem:
+                        heapq.heapreplace(exlist, exitem)
+                if not exlist or ritem != exlist[0]:
+                    total += 1
+                    yield ritem.dt
+                lastdt = ritem.dt
+            advance_iterator(ritem)
+            if rlist and rlist[0] is ritem:
+                heapq.heapreplace(rlist, ritem)
+        self._len = total
+
+
+
+
+class _rrulestr(object):
+    """ Parses a string representation of a recurrence rule or set of
+    recurrence rules.
+
+    :param s:
+        Required, a string defining one or more recurrence rules.
+
+    :param dtstart:
+        If given, used as the default recurrence start if not specified in the
+        rule string.
+
+    :param cache:
+        If set ``True`` caching of results will be enabled, improving
+        performance of multiple queries considerably.
+
+    :param unfold:
+        If set ``True`` indicates that a rule string is split over more
+        than one line and should be joined before processing.
+
+    :param forceset:
+        If set ``True`` forces a :class:`dateutil.rrule.rruleset` to
+        be returned.
+
+    :param compatible:
+        If set ``True`` forces ``unfold`` and ``forceset`` to be ``True``.
+
+    :param ignoretz:
+        If set ``True``, time zones in parsed strings are ignored and a naive
+        :class:`datetime.datetime` object is returned.
+
+    :param tzids:
+        If given, a callable or mapping used to retrieve a
+        :class:`datetime.tzinfo` from a string representation.
+        Defaults to :func:`dateutil.tz.gettz`.
+
+    :param tzinfos:
+        Additional time zone names / aliases which may be present in a string
+        representation.  See :func:`dateutil.parser.parse` for more
+        information.
+
+    :return:
+        Returns a :class:`dateutil.rrule.rruleset` or
+        :class:`dateutil.rrule.rrule`
+    """
+
+    _freq_map = {"YEARLY": YEARLY,
+                 "MONTHLY": MONTHLY,
+                 "WEEKLY": WEEKLY,
+                 "DAILY": DAILY,
+                 "HOURLY": HOURLY,
+                 "MINUTELY": MINUTELY,
+                 "SECONDLY": SECONDLY}
+
+    _weekday_map = {"MO": 0, "TU": 1, "WE": 2, "TH": 3,
+                    "FR": 4, "SA": 5, "SU": 6}
+
+    def _handle_int(self, rrkwargs, name, value, **kwargs):
+        rrkwargs[name.lower()] = int(value)
+
+    def _handle_int_list(self, rrkwargs, name, value, **kwargs):
+        rrkwargs[name.lower()] = [int(x) for x in value.split(',')]
+
+    _handle_INTERVAL = _handle_int
+    _handle_COUNT = _handle_int
+    _handle_BYSETPOS = _handle_int_list
+    _handle_BYMONTH = _handle_int_list
+    _handle_BYMONTHDAY = _handle_int_list
+    _handle_BYYEARDAY = _handle_int_list
+    _handle_BYEASTER = _handle_int_list
+    _handle_BYWEEKNO = _handle_int_list
+    _handle_BYHOUR = _handle_int_list
+    _handle_BYMINUTE = _handle_int_list
+    _handle_BYSECOND = _handle_int_list
+
+    def _handle_FREQ(self, rrkwargs, name, value, **kwargs):
+        rrkwargs["freq"] = self._freq_map[value]
+
+    def _handle_UNTIL(self, rrkwargs, name, value, **kwargs):
+        global parser
+        if not parser:
+            from dateutil import parser
+        try:
+            rrkwargs["until"] = parser.parse(value,
+                                             ignoretz=kwargs.get("ignoretz"),
+                                             tzinfos=kwargs.get("tzinfos"))
+        except ValueError:
+            raise ValueError("invalid until date")
+
+    def _handle_WKST(self, rrkwargs, name, value, **kwargs):
+        rrkwargs["wkst"] = self._weekday_map[value]
+
+    def _handle_BYWEEKDAY(self, rrkwargs, name, value, **kwargs):
+        """
+        Two ways to specify this: +1MO or MO(+1)
+        """
+        l = []
+        for wday in value.split(','):
+            if '(' in wday:
+                # If it's of the form TH(+1), etc.
+                splt = wday.split('(')
+                w = splt[0]
+                n = int(splt[1][:-1])
+            elif len(wday):
+                # If it's of the form +1MO
+                for i in range(len(wday)):
+                    if wday[i] not in '+-0123456789':
+                        break
+                n = wday[:i] or None
+                w = wday[i:]
+                if n:
+                    n = int(n)
+            else:
+                raise ValueError("Invalid (empty) BYDAY specification.")
+
+            l.append(weekdays[self._weekday_map[w]](n))
+        rrkwargs["byweekday"] = l
+
+    _handle_BYDAY = _handle_BYWEEKDAY
+
+    def _parse_rfc_rrule(self, line,
+                         dtstart=None,
+                         cache=False,
+                         ignoretz=False,
+                         tzinfos=None):
+        if line.find(':') != -1:
+            name, value = line.split(':')
+            if name != "RRULE":
+                raise ValueError("unknown parameter name")
+        else:
+            value = line
+        rrkwargs = {}
+        for pair in value.split(';'):
+            name, value = pair.split('=')
+            name = name.upper()
+            value = value.upper()
+            try:
+                getattr(self, "_handle_"+name)(rrkwargs, name, value,
+                                               ignoretz=ignoretz,
+                                               tzinfos=tzinfos)
+            except AttributeError:
+                raise ValueError("unknown parameter '%s'" % name)
+            except (KeyError, ValueError):
+                raise ValueError("invalid '%s': %s" % (name, value))
+        return rrule(dtstart=dtstart, cache=cache, **rrkwargs)
+
+    def _parse_date_value(self, date_value, parms, rule_tzids,
+                          ignoretz, tzids, tzinfos):
+        global parser
+        if not parser:
+            from dateutil import parser
+
+        datevals = []
+        value_found = False
+        TZID = None
+
+        for parm in parms:
+            if parm.startswith("TZID="):
+                try:
+                    tzkey = rule_tzids[parm.split('TZID=')[-1]]
+                except KeyError:
+                    continue
+                if tzids is None:
+                    from . import tz
+                    tzlookup = tz.gettz
+                elif callable(tzids):
+                    tzlookup = tzids
+                else:
+                    tzlookup = getattr(tzids, 'get', None)
+                    if tzlookup is None:
+                        msg = ('tzids must be a callable, mapping, or None, '
+                               'not %s' % tzids)
+                        raise ValueError(msg)
+
+                TZID = tzlookup(tzkey)
+                continue
+
+            # RFC 5445 3.8.2.4: The VALUE parameter is optional, but may be found
+            # only once.
+            if parm not in {"VALUE=DATE-TIME", "VALUE=DATE"}:
+                raise ValueError("unsupported parm: " + parm)
+            else:
+                if value_found:
+                    msg = ("Duplicate value parameter found in: " + parm)
+                    raise ValueError(msg)
+                value_found = True
+
+        for datestr in date_value.split(','):
+            date = parser.parse(datestr, ignoretz=ignoretz, tzinfos=tzinfos)
+            if TZID is not None:
+                if date.tzinfo is None:
+                    date = date.replace(tzinfo=TZID)
+                else:
+                    raise ValueError('DTSTART/EXDATE specifies multiple timezone')
+            datevals.append(date)
+
+        return datevals
+
+    def _parse_rfc(self, s,
+                   dtstart=None,
+                   cache=False,
+                   unfold=False,
+                   forceset=False,
+                   compatible=False,
+                   ignoretz=False,
+                   tzids=None,
+                   tzinfos=None):
+        global parser
+        if compatible:
+            forceset = True
+            unfold = True
+
+        TZID_NAMES = dict(map(
+            lambda x: (x.upper(), x),
+            re.findall('TZID=(?P<name>[^:]+):', s)
+        ))
+        s = s.upper()
+        if not s.strip():
+            raise ValueError("empty string")
+        if unfold:
+            lines = s.splitlines()
+            i = 0
+            while i < len(lines):
+                line = lines[i].rstrip()
+                if not line:
+                    del lines[i]
+                elif i > 0 and line[0] == " ":
+                    lines[i-1] += line[1:]
+                    del lines[i]
+                else:
+                    i += 1
+        else:
+            lines = s.split()
+        if (not forceset and len(lines) == 1 and (s.find(':') == -1 or
+                                                  s.startswith('RRULE:'))):
+            return self._parse_rfc_rrule(lines[0], cache=cache,
+                                         dtstart=dtstart, ignoretz=ignoretz,
+                                         tzinfos=tzinfos)
+        else:
+            rrulevals = []
+            rdatevals = []
+            exrulevals = []
+            exdatevals = []
+            for line in lines:
+                if not line:
+                    continue
+                if line.find(':') == -1:
+                    name = "RRULE"
+                    value = line
+                else:
+                    name, value = line.split(':', 1)
+                parms = name.split(';')
+                if not parms:
+                    raise ValueError("empty property name")
+                name = parms[0]
+                parms = parms[1:]
+                if name == "RRULE":
+                    for parm in parms:
+                        raise ValueError("unsupported RRULE parm: "+parm)
+                    rrulevals.append(value)
+                elif name == "RDATE":
+                    for parm in parms:
+                        if parm != "VALUE=DATE-TIME":
+                            raise ValueError("unsupported RDATE parm: "+parm)
+                    rdatevals.append(value)
+                elif name == "EXRULE":
+                    for parm in parms:
+                        raise ValueError("unsupported EXRULE parm: "+parm)
+                    exrulevals.append(value)
+                elif name == "EXDATE":
+                    exdatevals.extend(
+                        self._parse_date_value(value, parms,
+                                               TZID_NAMES, ignoretz,
+                                               tzids, tzinfos)
+                    )
+                elif name == "DTSTART":
+                    dtvals = self._parse_date_value(value, parms, TZID_NAMES,
+                                                    ignoretz, tzids, tzinfos)
+                    if len(dtvals) != 1:
+                        raise ValueError("Multiple DTSTART values specified:" +
+                                         value)
+                    dtstart = dtvals[0]
+                else:
+                    raise ValueError("unsupported property: "+name)
+            if (forceset or len(rrulevals) > 1 or rdatevals
+                    or exrulevals or exdatevals):
+                if not parser and (rdatevals or exdatevals):
+                    from dateutil import parser
+                rset = rruleset(cache=cache)
+                for value in rrulevals:
+                    rset.rrule(self._parse_rfc_rrule(value, dtstart=dtstart,
+                                                     ignoretz=ignoretz,
+                                                     tzinfos=tzinfos))
+                for value in rdatevals:
+                    for datestr in value.split(','):
+                        rset.rdate(parser.parse(datestr,
+                                                ignoretz=ignoretz,
+                                                tzinfos=tzinfos))
+                for value in exrulevals:
+                    rset.exrule(self._parse_rfc_rrule(value, dtstart=dtstart,
+                                                      ignoretz=ignoretz,
+                                                      tzinfos=tzinfos))
+                for value in exdatevals:
+                    rset.exdate(value)
+                if compatible and dtstart:
+                    rset.rdate(dtstart)
+                return rset
+            else:
+                return self._parse_rfc_rrule(rrulevals[0],
+                                             dtstart=dtstart,
+                                             cache=cache,
+                                             ignoretz=ignoretz,
+                                             tzinfos=tzinfos)
+
+    def __call__(self, s, **kwargs):
+        return self._parse_rfc(s, **kwargs)
+
+
+rrulestr = _rrulestr()
+
+# vim:ts=4:sw=4:et

venv/lib/python3.10/site-packages/dateutil/tz/__init__.py

@@ -0,0 +1,12 @@
+# -*- coding: utf-8 -*-
+from .tz import *
+from .tz import __doc__
+
+__all__ = ["tzutc", "tzoffset", "tzlocal", "tzfile", "tzrange",
+           "tzstr", "tzical", "tzwin", "tzwinlocal", "gettz",
+           "enfold", "datetime_ambiguous", "datetime_exists",
+           "resolve_imaginary", "UTC", "DeprecatedTzFormatWarning"]
+
+
+class DeprecatedTzFormatWarning(Warning):
+    """Warning raised when time zones are parsed from deprecated formats."""

venv/lib/python3.10/site-packages/dateutil/tz/_common.py

@@ -0,0 +1,419 @@
+from six import PY2
+
+from functools import wraps
+
+from datetime import datetime, timedelta, tzinfo
+
+
+ZERO = timedelta(0)
+
+__all__ = ['tzname_in_python2', 'enfold']
+
+
+def tzname_in_python2(namefunc):
+    """Change unicode output into bytestrings in Python 2
+
+    tzname() API changed in Python 3. It used to return bytes, but was changed
+    to unicode strings
+    """
+    if PY2:
+        @wraps(namefunc)
+        def adjust_encoding(*args, **kwargs):
+            name = namefunc(*args, **kwargs)
+            if name is not None:
+                name = name.encode()
+
+            return name
+
+        return adjust_encoding
+    else:
+        return namefunc
+
+
+# The following is adapted from Alexander Belopolsky's tz library
+# https://github.com/abalkin/tz
+if hasattr(datetime, 'fold'):
+    # This is the pre-python 3.6 fold situation
+    def enfold(dt, fold=1):
+        """
+        Provides a unified interface for assigning the ``fold`` attribute to
+        datetimes both before and after the implementation of PEP-495.
+
+        :param fold:
+            The value for the ``fold`` attribute in the returned datetime. This
+            should be either 0 or 1.
+
+        :return:
+            Returns an object for which ``getattr(dt, 'fold', 0)`` returns
+            ``fold`` for all versions of Python. In versions prior to
+            Python 3.6, this is a ``_DatetimeWithFold`` object, which is a
+            subclass of :py:class:`datetime.datetime` with the ``fold``
+            attribute added, if ``fold`` is 1.
+
+        .. versionadded:: 2.6.0
+        """
+        return dt.replace(fold=fold)
+
+else:
+    class _DatetimeWithFold(datetime):
+        """
+        This is a class designed to provide a PEP 495-compliant interface for
+        Python versions before 3.6. It is used only for dates in a fold, so
+        the ``fold`` attribute is fixed at ``1``.
+
+        .. versionadded:: 2.6.0
+        """
+        __slots__ = ()
+
+        def replace(self, *args, **kwargs):
+            """
+            Return a datetime with the same attributes, except for those
+            attributes given new values by whichever keyword arguments are
+            specified. Note that tzinfo=None can be specified to create a naive
+            datetime from an aware datetime with no conversion of date and time
+            data.
+
+            This is reimplemented in ``_DatetimeWithFold`` because pypy3 will
+            return a ``datetime.datetime`` even if ``fold`` is unchanged.
+            """
+            argnames = (
+                'year', 'month', 'day', 'hour', 'minute', 'second',
+                'microsecond', 'tzinfo'
+            )
+
+            for arg, argname in zip(args, argnames):
+                if argname in kwargs:
+                    raise TypeError('Duplicate argument: {}'.format(argname))
+
+                kwargs[argname] = arg
+
+            for argname in argnames:
+                if argname not in kwargs:
+                    kwargs[argname] = getattr(self, argname)
+
+            dt_class = self.__class__ if kwargs.get('fold', 1) else datetime
+
+            return dt_class(**kwargs)
+
+        @property
+        def fold(self):
+            return 1
+
+    def enfold(dt, fold=1):
+        """
+        Provides a unified interface for assigning the ``fold`` attribute to
+        datetimes both before and after the implementation of PEP-495.
+
+        :param fold:
+            The value for the ``fold`` attribute in the returned datetime. This
+            should be either 0 or 1.
+
+        :return:
+            Returns an object for which ``getattr(dt, 'fold', 0)`` returns
+            ``fold`` for all versions of Python. In versions prior to
+            Python 3.6, this is a ``_DatetimeWithFold`` object, which is a
+            subclass of :py:class:`datetime.datetime` with the ``fold``
+            attribute added, if ``fold`` is 1.
+
+        .. versionadded:: 2.6.0
+        """
+        if getattr(dt, 'fold', 0) == fold:
+            return dt
+
+        args = dt.timetuple()[:6]
+        args += (dt.microsecond, dt.tzinfo)
+
+        if fold:
+            return _DatetimeWithFold(*args)
+        else:
+            return datetime(*args)
+
+
+def _validate_fromutc_inputs(f):
+    """
+    The CPython version of ``fromutc`` checks that the input is a ``datetime``
+    object and that ``self`` is attached as its ``tzinfo``.
+    """
+    @wraps(f)
+    def fromutc(self, dt):
+        if not isinstance(dt, datetime):
+            raise TypeError("fromutc() requires a datetime argument")
+        if dt.tzinfo is not self:
+            raise ValueError("dt.tzinfo is not self")
+
+        return f(self, dt)
+
+    return fromutc
+
+
+class _tzinfo(tzinfo):
+    """
+    Base class for all ``dateutil`` ``tzinfo`` objects.
+    """
+
+    def is_ambiguous(self, dt):
+        """
+        Whether or not the "wall time" of a given datetime is ambiguous in this
+        zone.
+
+        :param dt:
+            A :py:class:`datetime.datetime`, naive or time zone aware.
+
+
+        :return:
+            Returns ``True`` if ambiguous, ``False`` otherwise.
+
+        .. versionadded:: 2.6.0
+        """
+
+        dt = dt.replace(tzinfo=self)
+
+        wall_0 = enfold(dt, fold=0)
+        wall_1 = enfold(dt, fold=1)
+
+        same_offset = wall_0.utcoffset() == wall_1.utcoffset()
+        same_dt = wall_0.replace(tzinfo=None) == wall_1.replace(tzinfo=None)
+
+        return same_dt and not same_offset
+
+    def _fold_status(self, dt_utc, dt_wall):
+        """
+        Determine the fold status of a "wall" datetime, given a representation
+        of the same datetime as a (naive) UTC datetime. This is calculated based
+        on the assumption that ``dt.utcoffset() - dt.dst()`` is constant for all
+        datetimes, and that this offset is the actual number of hours separating
+        ``dt_utc`` and ``dt_wall``.
+
+        :param dt_utc:
+            Representation of the datetime as UTC
+
+        :param dt_wall:
+            Representation of the datetime as "wall time". This parameter must
+            either have a `fold` attribute or have a fold-naive
+            :class:`datetime.tzinfo` attached, otherwise the calculation may
+            fail.
+        """
+        if self.is_ambiguous(dt_wall):
+            delta_wall = dt_wall - dt_utc
+            _fold = int(delta_wall == (dt_utc.utcoffset() - dt_utc.dst()))
+        else:
+            _fold = 0
+
+        return _fold
+
+    def _fold(self, dt):
+        return getattr(dt, 'fold', 0)
+
+    def _fromutc(self, dt):
+        """
+        Given a timezone-aware datetime in a given timezone, calculates a
+        timezone-aware datetime in a new timezone.
+
+        Since this is the one time that we *know* we have an unambiguous
+        datetime object, we take this opportunity to determine whether the
+        datetime is ambiguous and in a "fold" state (e.g. if it's the first
+        occurrence, chronologically, of the ambiguous datetime).
+
+        :param dt:
+            A timezone-aware :class:`datetime.datetime` object.
+        """
+
+        # Re-implement the algorithm from Python's datetime.py
+        dtoff = dt.utcoffset()
+        if dtoff is None:
+            raise ValueError("fromutc() requires a non-None utcoffset() "
+                             "result")
+
+        # The original datetime.py code assumes that `dst()` defaults to
+        # zero during ambiguous times. PEP 495 inverts this presumption, so
+        # for pre-PEP 495 versions of python, we need to tweak the algorithm.
+        dtdst = dt.dst()
+        if dtdst is None:
+            raise ValueError("fromutc() requires a non-None dst() result")
+        delta = dtoff - dtdst
+
+        dt += delta
+        # Set fold=1 so we can default to being in the fold for
+        # ambiguous dates.
+        dtdst = enfold(dt, fold=1).dst()
+        if dtdst is None:
+            raise ValueError("fromutc(): dt.dst gave inconsistent "
+                             "results; cannot convert")
+        return dt + dtdst
+
+    @_validate_fromutc_inputs
+    def fromutc(self, dt):
+        """
+        Given a timezone-aware datetime in a given timezone, calculates a
+        timezone-aware datetime in a new timezone.
+
+        Since this is the one time that we *know* we have an unambiguous
+        datetime object, we take this opportunity to determine whether the
+        datetime is ambiguous and in a "fold" state (e.g. if it's the first
+        occurrence, chronologically, of the ambiguous datetime).
+
+        :param dt:
+            A timezone-aware :class:`datetime.datetime` object.
+        """
+        dt_wall = self._fromutc(dt)
+
+        # Calculate the fold status given the two datetimes.
+        _fold = self._fold_status(dt, dt_wall)
+
+        # Set the default fold value for ambiguous dates
+        return enfold(dt_wall, fold=_fold)
+
+
+class tzrangebase(_tzinfo):
+    """
+    This is an abstract base class for time zones represented by an annual
+    transition into and out of DST. Child classes should implement the following
+    methods:
+
+        * ``__init__(self, *args, **kwargs)``
+        * ``transitions(self, year)`` - this is expected to return a tuple of
+          datetimes representing the DST on and off transitions in standard
+          time.
+
+    A fully initialized ``tzrangebase`` subclass should also provide the
+    following attributes:
+        * ``hasdst``: Boolean whether or not the zone uses DST.
+        * ``_dst_offset`` / ``_std_offset``: :class:`datetime.timedelta` objects
+          representing the respective UTC offsets.
+        * ``_dst_abbr`` / ``_std_abbr``: Strings representing the timezone short
+          abbreviations in DST and STD, respectively.
+        * ``_hasdst``: Whether or not the zone has DST.
+
+    .. versionadded:: 2.6.0
+    """
+    def __init__(self):
+        raise NotImplementedError('tzrangebase is an abstract base class')
+
+    def utcoffset(self, dt):
+        isdst = self._isdst(dt)
+
+        if isdst is None:
+            return None
+        elif isdst:
+            return self._dst_offset
+        else:
+            return self._std_offset
+
+    def dst(self, dt):
+        isdst = self._isdst(dt)
+
+        if isdst is None:
+            return None
+        elif isdst:
+            return self._dst_base_offset
+        else:
+            return ZERO
+
+    @tzname_in_python2
+    def tzname(self, dt):
+        if self._isdst(dt):
+            return self._dst_abbr
+        else:
+            return self._std_abbr
+
+    def fromutc(self, dt):
+        """ Given a datetime in UTC, return local time """
+        if not isinstance(dt, datetime):
+            raise TypeError("fromutc() requires a datetime argument")
+
+        if dt.tzinfo is not self:
+            raise ValueError("dt.tzinfo is not self")
+
+        # Get transitions - if there are none, fixed offset
+        transitions = self.transitions(dt.year)
+        if transitions is None:
+            return dt + self.utcoffset(dt)
+
+        # Get the transition times in UTC
+        dston, dstoff = transitions
+
+        dston -= self._std_offset
+        dstoff -= self._std_offset
+
+        utc_transitions = (dston, dstoff)
+        dt_utc = dt.replace(tzinfo=None)
+
+        isdst = self._naive_isdst(dt_utc, utc_transitions)
+
+        if isdst:
+            dt_wall = dt + self._dst_offset
+        else:
+            dt_wall = dt + self._std_offset
+
+        _fold = int(not isdst and self.is_ambiguous(dt_wall))
+
+        return enfold(dt_wall, fold=_fold)
+
+    def is_ambiguous(self, dt):
+        """
+        Whether or not the "wall time" of a given datetime is ambiguous in this
+        zone.
+
+        :param dt:
+            A :py:class:`datetime.datetime`, naive or time zone aware.
+
+
+        :return:
+            Returns ``True`` if ambiguous, ``False`` otherwise.
+
+        .. versionadded:: 2.6.0
+        """
+        if not self.hasdst:
+            return False
+
+        start, end = self.transitions(dt.year)
+
+        dt = dt.replace(tzinfo=None)
+        return (end <= dt < end + self._dst_base_offset)
+
+    def _isdst(self, dt):
+        if not self.hasdst:
+            return False
+        elif dt is None:
+            return None
+
+        transitions = self.transitions(dt.year)
+
+        if transitions is None:
+            return False
+
+        dt = dt.replace(tzinfo=None)
+
+        isdst = self._naive_isdst(dt, transitions)
+
+        # Handle ambiguous dates
+        if not isdst and self.is_ambiguous(dt):
+            return not self._fold(dt)
+        else:
+            return isdst
+
+    def _naive_isdst(self, dt, transitions):
+        dston, dstoff = transitions
+
+        dt = dt.replace(tzinfo=None)
+
+        if dston < dstoff:
+            isdst = dston <= dt < dstoff
+        else:
+            isdst = not dstoff <= dt < dston
+
+        return isdst
+
+    @property
+    def _dst_base_offset(self):
+        return self._dst_offset - self._std_offset
+
+    __hash__ = None
+
+    def __ne__(self, other):
+        return not (self == other)
+
+    def __repr__(self):
+        return "%s(...)" % self.__class__.__name__
+
+    __reduce__ = object.__reduce__

venv/lib/python3.10/site-packages/dateutil/tz/_factories.py

@@ -0,0 +1,80 @@
+from datetime import timedelta
+import weakref
+from collections import OrderedDict
+
+from six.moves import _thread
+
+
+class _TzSingleton(type):
+    def __init__(cls, *args, **kwargs):
+        cls.__instance = None
+        super(_TzSingleton, cls).__init__(*args, **kwargs)
+
+    def __call__(cls):
+        if cls.__instance is None:
+            cls.__instance = super(_TzSingleton, cls).__call__()
+        return cls.__instance
+
+
+class _TzFactory(type):
+    def instance(cls, *args, **kwargs):
+        """Alternate constructor that returns a fresh instance"""
+        return type.__call__(cls, *args, **kwargs)
+
+
+class _TzOffsetFactory(_TzFactory):
+    def __init__(cls, *args, **kwargs):
+        cls.__instances = weakref.WeakValueDictionary()
+        cls.__strong_cache = OrderedDict()
+        cls.__strong_cache_size = 8
+
+        cls._cache_lock = _thread.allocate_lock()
+
+    def __call__(cls, name, offset):
+        if isinstance(offset, timedelta):
+            key = (name, offset.total_seconds())
+        else:
+            key = (name, offset)
+
+        instance = cls.__instances.get(key, None)
+        if instance is None:
+            instance = cls.__instances.setdefault(key,
+                                                  cls.instance(name, offset))
+
+        # This lock may not be necessary in Python 3. See GH issue #901
+        with cls._cache_lock:
+            cls.__strong_cache[key] = cls.__strong_cache.pop(key, instance)
+
+            # Remove an item if the strong cache is overpopulated
+            if len(cls.__strong_cache) > cls.__strong_cache_size:
+                cls.__strong_cache.popitem(last=False)
+
+        return instance
+
+
+class _TzStrFactory(_TzFactory):
+    def __init__(cls, *args, **kwargs):
+        cls.__instances = weakref.WeakValueDictionary()
+        cls.__strong_cache = OrderedDict()
+        cls.__strong_cache_size = 8
+
+        cls.__cache_lock = _thread.allocate_lock()
+
+    def __call__(cls, s, posix_offset=False):
+        key = (s, posix_offset)
+        instance = cls.__instances.get(key, None)
+
+        if instance is None:
+            instance = cls.__instances.setdefault(key,
+                cls.instance(s, posix_offset))
+
+        # This lock may not be necessary in Python 3. See GH issue #901
+        with cls.__cache_lock:
+            cls.__strong_cache[key] = cls.__strong_cache.pop(key, instance)
+
+            # Remove an item if the strong cache is overpopulated
+            if len(cls.__strong_cache) > cls.__strong_cache_size:
+                cls.__strong_cache.popitem(last=False)
+
+        return instance
+

venv/lib/python3.10/site-packages/dateutil/tz/tz.py

@@ -0,0 +1,1849 @@
+# -*- coding: utf-8 -*-
+"""
+This module offers timezone implementations subclassing the abstract
+:py:class:`datetime.tzinfo` type. There are classes to handle tzfile format
+files (usually are in :file:`/etc/localtime`, :file:`/usr/share/zoneinfo`,
+etc), TZ environment string (in all known formats), given ranges (with help
+from relative deltas), local machine timezone, fixed offset timezone, and UTC
+timezone.
+"""
+import datetime
+import struct
+import time
+import sys
+import os
+import bisect
+import weakref
+from collections import OrderedDict
+
+import six
+from six import string_types
+from six.moves import _thread
+from ._common import tzname_in_python2, _tzinfo
+from ._common import tzrangebase, enfold
+from ._common import _validate_fromutc_inputs
+
+from ._factories import _TzSingleton, _TzOffsetFactory
+from ._factories import _TzStrFactory
+try:
+    from .win import tzwin, tzwinlocal
+except ImportError:
+    tzwin = tzwinlocal = None
+
+# For warning about rounding tzinfo
+from warnings import warn
+
+ZERO = datetime.timedelta(0)
+EPOCH = datetime.datetime(1970, 1, 1, 0, 0)
+EPOCHORDINAL = EPOCH.toordinal()
+
+
+@six.add_metaclass(_TzSingleton)
+class tzutc(datetime.tzinfo):
+    """
+    This is a tzinfo object that represents the UTC time zone.
+
+    **Examples:**
+
+    .. doctest::
+
+        >>> from datetime import *
+        >>> from dateutil.tz import *
+
+        >>> datetime.now()
+        datetime.datetime(2003, 9, 27, 9, 40, 1, 521290)
+
+        >>> datetime.now(tzutc())
+        datetime.datetime(2003, 9, 27, 12, 40, 12, 156379, tzinfo=tzutc())
+
+        >>> datetime.now(tzutc()).tzname()
+        'UTC'
+
+    .. versionchanged:: 2.7.0
+        ``tzutc()`` is now a singleton, so the result of ``tzutc()`` will
+        always return the same object.
+
+        .. doctest::
+
+            >>> from dateutil.tz import tzutc, UTC
+            >>> tzutc() is tzutc()
+            True
+            >>> tzutc() is UTC
+            True
+    """
+    def utcoffset(self, dt):
+        return ZERO
+
+    def dst(self, dt):
+        return ZERO
+
+    @tzname_in_python2
+    def tzname(self, dt):
+        return "UTC"
+
+    def is_ambiguous(self, dt):
+        """
+        Whether or not the "wall time" of a given datetime is ambiguous in this
+        zone.
+
+        :param dt:
+            A :py:class:`datetime.datetime`, naive or time zone aware.
+
+
+        :return:
+            Returns ``True`` if ambiguous, ``False`` otherwise.
+
+        .. versionadded:: 2.6.0
+        """
+        return False
+
+    @_validate_fromutc_inputs
+    def fromutc(self, dt):
+        """
+        Fast track version of fromutc() returns the original ``dt`` object for
+        any valid :py:class:`datetime.datetime` object.
+        """
+        return dt
+
+    def __eq__(self, other):
+        if not isinstance(other, (tzutc, tzoffset)):
+            return NotImplemented
+
+        return (isinstance(other, tzutc) or
+                (isinstance(other, tzoffset) and other._offset == ZERO))
+
+    __hash__ = None
+
+    def __ne__(self, other):
+        return not (self == other)
+
+    def __repr__(self):
+        return "%s()" % self.__class__.__name__
+
+    __reduce__ = object.__reduce__
+
+
+#: Convenience constant providing a :class:`tzutc()` instance
+#:
+#: .. versionadded:: 2.7.0
+UTC = tzutc()
+
+
+@six.add_metaclass(_TzOffsetFactory)
+class tzoffset(datetime.tzinfo):
+    """
+    A simple class for representing a fixed offset from UTC.
+
+    :param name:
+        The timezone name, to be returned when ``tzname()`` is called.
+    :param offset:
+        The time zone offset in seconds, or (since version 2.6.0, represented
+        as a :py:class:`datetime.timedelta` object).
+    """
+    def __init__(self, name, offset):
+        self._name = name
+
+        try:
+            # Allow a timedelta
+            offset = offset.total_seconds()
+        except (TypeError, AttributeError):
+            pass
+
+        self._offset = datetime.timedelta(seconds=_get_supported_offset(offset))
+
+    def utcoffset(self, dt):
+        return self._offset
+
+    def dst(self, dt):
+        return ZERO
+
+    @tzname_in_python2
+    def tzname(self, dt):
+        return self._name
+
+    @_validate_fromutc_inputs
+    def fromutc(self, dt):
+        return dt + self._offset
+
+    def is_ambiguous(self, dt):
+        """
+        Whether or not the "wall time" of a given datetime is ambiguous in this
+        zone.
+
+        :param dt:
+            A :py:class:`datetime.datetime`, naive or time zone aware.
+        :return:
+            Returns ``True`` if ambiguous, ``False`` otherwise.
+
+        .. versionadded:: 2.6.0
+        """
+        return False
+
+    def __eq__(self, other):
+        if not isinstance(other, tzoffset):
+            return NotImplemented
+
+        return self._offset == other._offset
+
+    __hash__ = None
+
+    def __ne__(self, other):
+        return not (self == other)
+
+    def __repr__(self):
+        return "%s(%s, %s)" % (self.__class__.__name__,
+                               repr(self._name),
+                               int(self._offset.total_seconds()))
+
+    __reduce__ = object.__reduce__
+
+
+class tzlocal(_tzinfo):
+    """
+    A :class:`tzinfo` subclass built around the ``time`` timezone functions.
+    """
+    def __init__(self):
+        super(tzlocal, self).__init__()
+
+        self._std_offset = datetime.timedelta(seconds=-time.timezone)
+        if time.daylight:
+            self._dst_offset = datetime.timedelta(seconds=-time.altzone)
+        else:
+            self._dst_offset = self._std_offset
+
+        self._dst_saved = self._dst_offset - self._std_offset
+        self._hasdst = bool(self._dst_saved)
+        self._tznames = tuple(time.tzname)
+
+    def utcoffset(self, dt):
+        if dt is None and self._hasdst:
+            return None
+
+        if self._isdst(dt):
+            return self._dst_offset
+        else:
+            return self._std_offset
+
+    def dst(self, dt):
+        if dt is None and self._hasdst:
+            return None
+
+        if self._isdst(dt):
+            return self._dst_offset - self._std_offset
+        else:
+            return ZERO
+
+    @tzname_in_python2
+    def tzname(self, dt):
+        return self._tznames[self._isdst(dt)]
+
+    def is_ambiguous(self, dt):
+        """
+        Whether or not the "wall time" of a given datetime is ambiguous in this
+        zone.
+
+        :param dt:
+            A :py:class:`datetime.datetime`, naive or time zone aware.
+
+
+        :return:
+            Returns ``True`` if ambiguous, ``False`` otherwise.
+
+        .. versionadded:: 2.6.0
+        """
+        naive_dst = self._naive_is_dst(dt)
+        return (not naive_dst and
+                (naive_dst != self._naive_is_dst(dt - self._dst_saved)))
+
+    def _naive_is_dst(self, dt):
+        timestamp = _datetime_to_timestamp(dt)
+        return time.localtime(timestamp + time.timezone).tm_isdst
+
+    def _isdst(self, dt, fold_naive=True):
+        # We can't use mktime here. It is unstable when deciding if
+        # the hour near to a change is DST or not.
+        #
+        # timestamp = time.mktime((dt.year, dt.month, dt.day, dt.hour,
+        #                         dt.minute, dt.second, dt.weekday(), 0, -1))
+        # return time.localtime(timestamp).tm_isdst
+        #
+        # The code above yields the following result:
+        #
+        # >>> import tz, datetime
+        # >>> t = tz.tzlocal()
+        # >>> datetime.datetime(2003,2,15,23,tzinfo=t).tzname()
+        # 'BRDT'
+        # >>> datetime.datetime(2003,2,16,0,tzinfo=t).tzname()
+        # 'BRST'
+        # >>> datetime.datetime(2003,2,15,23,tzinfo=t).tzname()
+        # 'BRST'
+        # >>> datetime.datetime(2003,2,15,22,tzinfo=t).tzname()
+        # 'BRDT'
+        # >>> datetime.datetime(2003,2,15,23,tzinfo=t).tzname()
+        # 'BRDT'
+        #
+        # Here is a more stable implementation:
+        #
+        if not self._hasdst:
+            return False
+
+        # Check for ambiguous times:
+        dstval = self._naive_is_dst(dt)
+        fold = getattr(dt, 'fold', None)
+
+        if self.is_ambiguous(dt):
+            if fold is not None:
+                return not self._fold(dt)
+            else:
+                return True
+
+        return dstval
+
+    def __eq__(self, other):
+        if isinstance(other, tzlocal):
+            return (self._std_offset == other._std_offset and
+                    self._dst_offset == other._dst_offset)
+        elif isinstance(other, tzutc):
+            return (not self._hasdst and
+                    self._tznames[0] in {'UTC', 'GMT'} and
+                    self._std_offset == ZERO)
+        elif isinstance(other, tzoffset):
+            return (not self._hasdst and
+                    self._tznames[0] == other._name and
+                    self._std_offset == other._offset)
+        else:
+            return NotImplemented
+
+    __hash__ = None
+
+    def __ne__(self, other):
+        return not (self == other)
+
+    def __repr__(self):
+        return "%s()" % self.__class__.__name__
+
+    __reduce__ = object.__reduce__
+
+
+class _ttinfo(object):
+    __slots__ = ["offset", "delta", "isdst", "abbr",
+                 "isstd", "isgmt", "dstoffset"]
+
+    def __init__(self):
+        for attr in self.__slots__:
+            setattr(self, attr, None)
+
+    def __repr__(self):
+        l = []
+        for attr in self.__slots__:
+            value = getattr(self, attr)
+            if value is not None:
+                l.append("%s=%s" % (attr, repr(value)))
+        return "%s(%s)" % (self.__class__.__name__, ", ".join(l))
+
+    def __eq__(self, other):
+        if not isinstance(other, _ttinfo):
+            return NotImplemented
+
+        return (self.offset == other.offset and
+                self.delta == other.delta and
+                self.isdst == other.isdst and
+                self.abbr == other.abbr and
+                self.isstd == other.isstd and
+                self.isgmt == other.isgmt and
+                self.dstoffset == other.dstoffset)
+
+    __hash__ = None
+
+    def __ne__(self, other):
+        return not (self == other)
+
+    def __getstate__(self):
+        state = {}
+        for name in self.__slots__:
+            state[name] = getattr(self, name, None)
+        return state
+
+    def __setstate__(self, state):
+        for name in self.__slots__:
+            if name in state:
+                setattr(self, name, state[name])
+
+
+class _tzfile(object):
+    """
+    Lightweight class for holding the relevant transition and time zone
+    information read from binary tzfiles.
+    """
+    attrs = ['trans_list', 'trans_list_utc', 'trans_idx', 'ttinfo_list',
+             'ttinfo_std', 'ttinfo_dst', 'ttinfo_before', 'ttinfo_first']
+
+    def __init__(self, **kwargs):
+        for attr in self.attrs:
+            setattr(self, attr, kwargs.get(attr, None))
+
+
+class tzfile(_tzinfo):
+    """
+    This is a ``tzinfo`` subclass that allows one to use the ``tzfile(5)``
+    format timezone files to extract current and historical zone information.
+
+    :param fileobj:
+        This can be an opened file stream or a file name that the time zone
+        information can be read from.
+
+    :param filename:
+        This is an optional parameter specifying the source of the time zone
+        information in the event that ``fileobj`` is a file object. If omitted
+        and ``fileobj`` is a file stream, this parameter will be set either to
+        ``fileobj``'s ``name`` attribute or to ``repr(fileobj)``.
+
+    See `Sources for Time Zone and Daylight Saving Time Data
+    <https://data.iana.org/time-zones/tz-link.html>`_ for more information.
+    Time zone files can be compiled from the `IANA Time Zone database files
+    <https://www.iana.org/time-zones>`_ with the `zic time zone compiler
+    <https://www.freebsd.org/cgi/man.cgi?query=zic&sektion=8>`_
+
+    .. note::
+
+        Only construct a ``tzfile`` directly if you have a specific timezone
+        file on disk that you want to read into a Python ``tzinfo`` object.
+        If you want to get a ``tzfile`` representing a specific IANA zone,
+        (e.g. ``'America/New_York'``), you should call
+        :func:`dateutil.tz.gettz` with the zone identifier.
+
+
+    **Examples:**
+
+    Using the US Eastern time zone as an example, we can see that a ``tzfile``
+    provides time zone information for the standard Daylight Saving offsets:
+
+    .. testsetup:: tzfile
+
+        from dateutil.tz import gettz
+        from datetime import datetime
+
+    .. doctest:: tzfile
+
+        >>> NYC = gettz('America/New_York')
+        >>> NYC
+        tzfile('/usr/share/zoneinfo/America/New_York')
+
+        >>> print(datetime(2016, 1, 3, tzinfo=NYC))     # EST
+        2016-01-03 00:00:00-05:00
+
+        >>> print(datetime(2016, 7, 7, tzinfo=NYC))     # EDT
+        2016-07-07 00:00:00-04:00
+
+
+    The ``tzfile`` structure contains a fully history of the time zone,
+    so historical dates will also have the right offsets. For example, before
+    the adoption of the UTC standards, New York used local solar  mean time:
+
+    .. doctest:: tzfile
+
+       >>> print(datetime(1901, 4, 12, tzinfo=NYC))    # LMT
+       1901-04-12 00:00:00-04:56
+
+    And during World War II, New York was on "Eastern War Time", which was a
+    state of permanent daylight saving time:
+
+    .. doctest:: tzfile
+
+        >>> print(datetime(1944, 2, 7, tzinfo=NYC))    # EWT
+        1944-02-07 00:00:00-04:00
+
+    """
+
+    def __init__(self, fileobj, filename=None):
+        super(tzfile, self).__init__()
+
+        file_opened_here = False
+        if isinstance(fileobj, string_types):
+            self._filename = fileobj
+            fileobj = open(fileobj, 'rb')
+            file_opened_here = True
+        elif filename is not None:
+            self._filename = filename
+        elif hasattr(fileobj, "name"):
+            self._filename = fileobj.name
+        else:
+            self._filename = repr(fileobj)
+
+        if fileobj is not None:
+            if not file_opened_here:
+                fileobj = _nullcontext(fileobj)
+
+            with fileobj as file_stream:
+                tzobj = self._read_tzfile(file_stream)
+
+            self._set_tzdata(tzobj)
+
+    def _set_tzdata(self, tzobj):
+        """ Set the time zone data of this object from a _tzfile object """
+        # Copy the relevant attributes over as private attributes
+        for attr in _tzfile.attrs:
+            setattr(self, '_' + attr, getattr(tzobj, attr))
+
+    def _read_tzfile(self, fileobj):
+        out = _tzfile()
+
+        # From tzfile(5):
+        #
+        # The time zone information files used by tzset(3)
+        # begin with the magic characters "TZif" to identify
+        # them as time zone information files, followed by
+        # sixteen bytes reserved for future use, followed by
+        # six four-byte values of type long, written in a
+        # ``standard'' byte order (the high-order  byte
+        # of the value is written first).
+        if fileobj.read(4).decode() != "TZif":
+            raise ValueError("magic not found")
+
+        fileobj.read(16)
+
+        (
+            # The number of UTC/local indicators stored in the file.
+            ttisgmtcnt,
+
+            # The number of standard/wall indicators stored in the file.
+            ttisstdcnt,
+
+            # The number of leap seconds for which data is
+            # stored in the file.
+            leapcnt,
+
+            # The number of "transition times" for which data
+            # is stored in the file.
+            timecnt,
+
+            # The number of "local time types" for which data
+            # is stored in the file (must not be zero).
+            typecnt,
+
+            # The  number  of  characters  of "time zone
+            # abbreviation strings" stored in the file.
+            charcnt,
+
+        ) = struct.unpack(">6l", fileobj.read(24))
+
+        # The above header is followed by tzh_timecnt four-byte
+        # values  of  type long,  sorted  in ascending order.
+        # These values are written in ``standard'' byte order.
+        # Each is used as a transition time (as  returned  by
+        # time(2)) at which the rules for computing local time
+        # change.
+
+        if timecnt:
+            out.trans_list_utc = list(struct.unpack(">%dl" % timecnt,
+                                                    fileobj.read(timecnt*4)))
+        else:
+            out.trans_list_utc = []
+
+        # Next come tzh_timecnt one-byte values of type unsigned
+        # char; each one tells which of the different types of
+        # ``local time'' types described in the file is associated
+        # with the same-indexed transition time. These values
+        # serve as indices into an array of ttinfo structures that
+        # appears next in the file.
+
+        if timecnt:
+            out.trans_idx = struct.unpack(">%dB" % timecnt,
+                                          fileobj.read(timecnt))
+        else:
+            out.trans_idx = []
+
+        # Each ttinfo structure is written as a four-byte value
+        # for tt_gmtoff  of  type long,  in  a  standard  byte
+        # order, followed  by a one-byte value for tt_isdst
+        # and a one-byte  value  for  tt_abbrind.   In  each
+        # structure, tt_gmtoff  gives  the  number  of
+        # seconds to be added to UTC, tt_isdst tells whether
+        # tm_isdst should be set by  localtime(3),  and
+        # tt_abbrind serves  as an index into the array of
+        # time zone abbreviation characters that follow the
+        # ttinfo structure(s) in the file.
+
+        ttinfo = []
+
+        for i in range(typecnt):
+            ttinfo.append(struct.unpack(">lbb", fileobj.read(6)))
+
+        abbr = fileobj.read(charcnt).decode()
+
+        # Then there are tzh_leapcnt pairs of four-byte
+        # values, written in  standard byte  order;  the
+        # first  value  of  each pair gives the time (as
+        # returned by time(2)) at which a leap second
+        # occurs;  the  second  gives the  total  number of
+        # leap seconds to be applied after the given time.
+        # The pairs of values are sorted in ascending order
+        # by time.
+
+        # Not used, for now (but seek for correct file position)
+        if leapcnt:
+            fileobj.seek(leapcnt * 8, os.SEEK_CUR)
+
+        # Then there are tzh_ttisstdcnt standard/wall
+        # indicators, each stored as a one-byte value;
+        # they tell whether the transition times associated
+        # with local time types were specified as standard
+        # time or wall clock time, and are used when
+        # a time zone file is used in handling POSIX-style
+        # time zone environment variables.
+
+        if ttisstdcnt:
+            isstd = struct.unpack(">%db" % ttisstdcnt,
+                                  fileobj.read(ttisstdcnt))
+
+        # Finally, there are tzh_ttisgmtcnt UTC/local
+        # indicators, each stored as a one-byte value;
+        # they tell whether the transition times associated
+        # with local time types were specified as UTC or
+        # local time, and are used when a time zone file
+        # is used in handling POSIX-style time zone envi-
+        # ronment variables.
+
+        if ttisgmtcnt:
+            isgmt = struct.unpack(">%db" % ttisgmtcnt,
+                                  fileobj.read(ttisgmtcnt))
+
+        # Build ttinfo list
+        out.ttinfo_list = []
+        for i in range(typecnt):
+            gmtoff, isdst, abbrind = ttinfo[i]
+            gmtoff = _get_supported_offset(gmtoff)
+            tti = _ttinfo()
+            tti.offset = gmtoff
+            tti.dstoffset = datetime.timedelta(0)
+            tti.delta = datetime.timedelta(seconds=gmtoff)
+            tti.isdst = isdst
+            tti.abbr = abbr[abbrind:abbr.find('\x00', abbrind)]
+            tti.isstd = (ttisstdcnt > i and isstd[i] != 0)
+            tti.isgmt = (ttisgmtcnt > i and isgmt[i] != 0)
+            out.ttinfo_list.append(tti)
+
+        # Replace ttinfo indexes for ttinfo objects.
+        out.trans_idx = [out.ttinfo_list[idx] for idx in out.trans_idx]
+
+        # Set standard, dst, and before ttinfos. before will be
+        # used when a given time is before any transitions,
+        # and will be set to the first non-dst ttinfo, or to
+        # the first dst, if all of them are dst.
+        out.ttinfo_std = None
+        out.ttinfo_dst = None
+        out.ttinfo_before = None
+        if out.ttinfo_list:
+            if not out.trans_list_utc:
+                out.ttinfo_std = out.ttinfo_first = out.ttinfo_list[0]
+            else:
+                for i in range(timecnt-1, -1, -1):
+                    tti = out.trans_idx[i]
+                    if not out.ttinfo_std and not tti.isdst:
+                        out.ttinfo_std = tti
+                    elif not out.ttinfo_dst and tti.isdst:
+                        out.ttinfo_dst = tti
+
+                    if out.ttinfo_std and out.ttinfo_dst:
+                        break
+                else:
+                    if out.ttinfo_dst and not out.ttinfo_std:
+                        out.ttinfo_std = out.ttinfo_dst
+
+                for tti in out.ttinfo_list:
+                    if not tti.isdst:
+                        out.ttinfo_before = tti
+                        break
+                else:
+                    out.ttinfo_before = out.ttinfo_list[0]
+
+        # Now fix transition times to become relative to wall time.
+        #
+        # I'm not sure about this. In my tests, the tz source file
+        # is setup to wall time, and in the binary file isstd and
+        # isgmt are off, so it should be in wall time. OTOH, it's
+        # always in gmt time. Let me know if you have comments
+        # about this.
+        lastdst = None
+        lastoffset = None
+        lastdstoffset = None
+        lastbaseoffset = None
+        out.trans_list = []
+
+        for i, tti in enumerate(out.trans_idx):
+            offset = tti.offset
+            dstoffset = 0
+
+            if lastdst is not None:
+                if tti.isdst:
+                    if not lastdst:
+                        dstoffset = offset - lastoffset
+
+                    if not dstoffset and lastdstoffset:
+                        dstoffset = lastdstoffset
+
+                    tti.dstoffset = datetime.timedelta(seconds=dstoffset)
+                    lastdstoffset = dstoffset
+
+            # If a time zone changes its base offset during a DST transition,
+            # then you need to adjust by the previous base offset to get the
+            # transition time in local time. Otherwise you use the current
+            # base offset. Ideally, I would have some mathematical proof of
+            # why this is true, but I haven't really thought about it enough.
+            baseoffset = offset - dstoffset
+            adjustment = baseoffset
+            if (lastbaseoffset is not None and baseoffset != lastbaseoffset
+                    and tti.isdst != lastdst):
+                # The base DST has changed
+                adjustment = lastbaseoffset
+
+            lastdst = tti.isdst
+            lastoffset = offset
+            lastbaseoffset = baseoffset
+
+            out.trans_list.append(out.trans_list_utc[i] + adjustment)
+
+        out.trans_idx = tuple(out.trans_idx)
+        out.trans_list = tuple(out.trans_list)
+        out.trans_list_utc = tuple(out.trans_list_utc)
+
+        return out
+
+    def _find_last_transition(self, dt, in_utc=False):
+        # If there's no list, there are no transitions to find
+        if not self._trans_list:
+            return None
+
+        timestamp = _datetime_to_timestamp(dt)
+
+        # Find where the timestamp fits in the transition list - if the
+        # timestamp is a transition time, it's part of the "after" period.
+        trans_list = self._trans_list_utc if in_utc else self._trans_list
+        idx = bisect.bisect_right(trans_list, timestamp)
+
+        # We want to know when the previous transition was, so subtract off 1
+        return idx - 1
+
+    def _get_ttinfo(self, idx):
+        # For no list or after the last transition, default to _ttinfo_std
+        if idx is None or (idx + 1) >= len(self._trans_list):
+            return self._ttinfo_std
+
+        # If there is a list and the time is before it, return _ttinfo_before
+        if idx < 0:
+            return self._ttinfo_before
+
+        return self._trans_idx[idx]
+
+    def _find_ttinfo(self, dt):
+        idx = self._resolve_ambiguous_time(dt)
+
+        return self._get_ttinfo(idx)
+
+    def fromutc(self, dt):
+        """
+        The ``tzfile`` implementation of :py:func:`datetime.tzinfo.fromutc`.
+
+        :param dt:
+            A :py:class:`datetime.datetime` object.
+
+        :raises TypeError:
+            Raised if ``dt`` is not a :py:class:`datetime.datetime` object.
+
+        :raises ValueError:
+            Raised if this is called with a ``dt`` which does not have this
+            ``tzinfo`` attached.
+
+        :return:
+            Returns a :py:class:`datetime.datetime` object representing the
+            wall time in ``self``'s time zone.
+        """
+        # These isinstance checks are in datetime.tzinfo, so we'll preserve
+        # them, even if we don't care about duck typing.
+        if not isinstance(dt, datetime.datetime):
+            raise TypeError("fromutc() requires a datetime argument")
+
+        if dt.tzinfo is not self:
+            raise ValueError("dt.tzinfo is not self")
+
+        # First treat UTC as wall time and get the transition we're in.
+        idx = self._find_last_transition(dt, in_utc=True)
+        tti = self._get_ttinfo(idx)
+
+        dt_out = dt + datetime.timedelta(seconds=tti.offset)
+
+        fold = self.is_ambiguous(dt_out, idx=idx)
+
+        return enfold(dt_out, fold=int(fold))
+
+    def is_ambiguous(self, dt, idx=None):
+        """
+        Whether or not the "wall time" of a given datetime is ambiguous in this
+        zone.
+
+        :param dt:
+            A :py:class:`datetime.datetime`, naive or time zone aware.
+
+
+        :return:
+            Returns ``True`` if ambiguous, ``False`` otherwise.
+
+        .. versionadded:: 2.6.0
+        """
+        if idx is None:
+            idx = self._find_last_transition(dt)
+
+        # Calculate the difference in offsets from current to previous
+        timestamp = _datetime_to_timestamp(dt)
+        tti = self._get_ttinfo(idx)
+
+        if idx is None or idx <= 0:
+            return False
+
+        od = self._get_ttinfo(idx - 1).offset - tti.offset
+        tt = self._trans_list[idx]          # Transition time
+
+        return timestamp < tt + od
+
+    def _resolve_ambiguous_time(self, dt):
+        idx = self._find_last_transition(dt)
+
+        # If we have no transitions, return the index
+        _fold = self._fold(dt)
+        if idx is None or idx == 0:
+            return idx
+
+        # If it's ambiguous and we're in a fold, shift to a different index.
+        idx_offset = int(not _fold and self.is_ambiguous(dt, idx))
+
+        return idx - idx_offset
+
+    def utcoffset(self, dt):
+        if dt is None:
+            return None
+
+        if not self._ttinfo_std:
+            return ZERO
+
+        return self._find_ttinfo(dt).delta
+
+    def dst(self, dt):
+        if dt is None:
+            return None
+
+        if not self._ttinfo_dst:
+            return ZERO
+
+        tti = self._find_ttinfo(dt)
+
+        if not tti.isdst:
+            return ZERO
+
+        # The documentation says that utcoffset()-dst() must
+        # be constant for every dt.
+        return tti.dstoffset
+
+    @tzname_in_python2
+    def tzname(self, dt):
+        if not self._ttinfo_std or dt is None:
+            return None
+        return self._find_ttinfo(dt).abbr
+
+    def __eq__(self, other):
+        if not isinstance(other, tzfile):
+            return NotImplemented
+        return (self._trans_list == other._trans_list and
+                self._trans_idx == other._trans_idx and
+                self._ttinfo_list == other._ttinfo_list)
+
+    __hash__ = None
+
+    def __ne__(self, other):
+        return not (self == other)
+
+    def __repr__(self):
+        return "%s(%s)" % (self.__class__.__name__, repr(self._filename))
+
+    def __reduce__(self):
+        return self.__reduce_ex__(None)
+
+    def __reduce_ex__(self, protocol):
+        return (self.__class__, (None, self._filename), self.__dict__)
+
+
+class tzrange(tzrangebase):
+    """
+    The ``tzrange`` object is a time zone specified by a set of offsets and
+    abbreviations, equivalent to the way the ``TZ`` variable can be specified
+    in POSIX-like systems, but using Python delta objects to specify DST
+    start, end and offsets.
+
+    :param stdabbr:
+        The abbreviation for standard time (e.g. ``'EST'``).
+
+    :param stdoffset:
+        An integer or :class:`datetime.timedelta` object or equivalent
+        specifying the base offset from UTC.
+
+        If unspecified, +00:00 is used.
+
+    :param dstabbr:
+        The abbreviation for DST / "Summer" time (e.g. ``'EDT'``).
+
+        If specified, with no other DST information, DST is assumed to occur
+        and the default behavior or ``dstoffset``, ``start`` and ``end`` is
+        used. If unspecified and no other DST information is specified, it
+        is assumed that this zone has no DST.
+
+        If this is unspecified and other DST information is *is* specified,
+        DST occurs in the zone but the time zone abbreviation is left
+        unchanged.
+
+    :param dstoffset:
+        A an integer or :class:`datetime.timedelta` object or equivalent
+        specifying the UTC offset during DST. If unspecified and any other DST
+        information is specified, it is assumed to be the STD offset +1 hour.
+
+    :param start:
+        A :class:`relativedelta.relativedelta` object or equivalent specifying
+        the time and time of year that daylight savings time starts. To
+        specify, for example, that DST starts at 2AM on the 2nd Sunday in
+        March, pass:
+
+            ``relativedelta(hours=2, month=3, day=1, weekday=SU(+2))``
+
+        If unspecified and any other DST information is specified, the default
+        value is 2 AM on the first Sunday in April.
+
+    :param end:
+        A :class:`relativedelta.relativedelta` object or equivalent
+        representing the time and time of year that daylight savings time
+        ends, with the same specification method as in ``start``. One note is
+        that this should point to the first time in the *standard* zone, so if
+        a transition occurs at 2AM in the DST zone and the clocks are set back
+        1 hour to 1AM, set the ``hours`` parameter to +1.
+
+
+    **Examples:**
+
+    .. testsetup:: tzrange
+
+        from dateutil.tz import tzrange, tzstr
+
+    .. doctest:: tzrange
+
+        >>> tzstr('EST5EDT') == tzrange("EST", -18000, "EDT")
+        True
+
+        >>> from dateutil.relativedelta import *
+        >>> range1 = tzrange("EST", -18000, "EDT")
+        >>> range2 = tzrange("EST", -18000, "EDT", -14400,
+        ...                  relativedelta(hours=+2, month=4, day=1,
+        ...                                weekday=SU(+1)),
+        ...                  relativedelta(hours=+1, month=10, day=31,
+        ...                                weekday=SU(-1)))
+        >>> tzstr('EST5EDT') == range1 == range2
+        True
+
+    """
+    def __init__(self, stdabbr, stdoffset=None,
+                 dstabbr=None, dstoffset=None,
+                 start=None, end=None):
+
+        global relativedelta
+        from dateutil import relativedelta
+
+        self._std_abbr = stdabbr
+        self._dst_abbr = dstabbr
+
+        try:
+            stdoffset = stdoffset.total_seconds()
+        except (TypeError, AttributeError):
+            pass
+
+        try:
+            dstoffset = dstoffset.total_seconds()
+        except (TypeError, AttributeError):
+            pass
+
+        if stdoffset is not None:
+            self._std_offset = datetime.timedelta(seconds=stdoffset)
+        else:
+            self._std_offset = ZERO
+
+        if dstoffset is not None:
+            self._dst_offset = datetime.timedelta(seconds=dstoffset)
+        elif dstabbr and stdoffset is not None:
+            self._dst_offset = self._std_offset + datetime.timedelta(hours=+1)
+        else:
+            self._dst_offset = ZERO
+
+        if dstabbr and start is None:
+            self._start_delta = relativedelta.relativedelta(
+                hours=+2, month=4, day=1, weekday=relativedelta.SU(+1))
+        else:
+            self._start_delta = start
+
+        if dstabbr and end is None:
+            self._end_delta = relativedelta.relativedelta(
+                hours=+1, month=10, day=31, weekday=relativedelta.SU(-1))
+        else:
+            self._end_delta = end
+
+        self._dst_base_offset_ = self._dst_offset - self._std_offset
+        self.hasdst = bool(self._start_delta)
+
+    def transitions(self, year):
+        """
+        For a given year, get the DST on and off transition times, expressed
+        always on the standard time side. For zones with no transitions, this
+        function returns ``None``.
+
+        :param year:
+            The year whose transitions you would like to query.
+
+        :return:
+            Returns a :class:`tuple` of :class:`datetime.datetime` objects,
+            ``(dston, dstoff)`` for zones with an annual DST transition, or
+            ``None`` for fixed offset zones.
+        """
+        if not self.hasdst:
+            return None
+
+        base_year = datetime.datetime(year, 1, 1)
+
+        start = base_year + self._start_delta
+        end = base_year + self._end_delta
+
+        return (start, end)
+
+    def __eq__(self, other):
+        if not isinstance(other, tzrange):
+            return NotImplemented
+
+        return (self._std_abbr == other._std_abbr and
+                self._dst_abbr == other._dst_abbr and
+                self._std_offset == other._std_offset and
+                self._dst_offset == other._dst_offset and
+                self._start_delta == other._start_delta and
+                self._end_delta == other._end_delta)
+
+    @property
+    def _dst_base_offset(self):
+        return self._dst_base_offset_
+
+
+@six.add_metaclass(_TzStrFactory)
+class tzstr(tzrange):
+    """
+    ``tzstr`` objects are time zone objects specified by a time-zone string as
+    it would be passed to a ``TZ`` variable on POSIX-style systems (see
+    the `GNU C Library: TZ Variable`_ for more details).
+
+    There is one notable exception, which is that POSIX-style time zones use an
+    inverted offset format, so normally ``GMT+3`` would be parsed as an offset
+    3 hours *behind* GMT. The ``tzstr`` time zone object will parse this as an
+    offset 3 hours *ahead* of GMT. If you would like to maintain the POSIX
+    behavior, pass a ``True`` value to ``posix_offset``.
+
+    The :class:`tzrange` object provides the same functionality, but is
+    specified using :class:`relativedelta.relativedelta` objects. rather than
+    strings.
+
+    :param s:
+        A time zone string in ``TZ`` variable format. This can be a
+        :class:`bytes` (2.x: :class:`str`), :class:`str` (2.x:
+        :class:`unicode`) or a stream emitting unicode characters
+        (e.g. :class:`StringIO`).
+
+    :param posix_offset:
+        Optional. If set to ``True``, interpret strings such as ``GMT+3`` or
+        ``UTC+3`` as being 3 hours *behind* UTC rather than ahead, per the
+        POSIX standard.
+
+    .. caution::
+
+        Prior to version 2.7.0, this function also supported time zones
+        in the format:
+
+            * ``EST5EDT,4,0,6,7200,10,0,26,7200,3600``
+            * ``EST5EDT,4,1,0,7200,10,-1,0,7200,3600``
+
+        This format is non-standard and has been deprecated; this function
+        will raise a :class:`DeprecatedTZFormatWarning` until
+        support is removed in a future version.
+
+    .. _`GNU C Library: TZ Variable`:
+        https://www.gnu.org/software/libc/manual/html_node/TZ-Variable.html
+    """
+    def __init__(self, s, posix_offset=False):
+        global parser
+        from dateutil.parser import _parser as parser
+
+        self._s = s
+
+        res = parser._parsetz(s)
+        if res is None or res.any_unused_tokens:
+            raise ValueError("unknown string format")
+
+        # Here we break the compatibility with the TZ variable handling.
+        # GMT-3 actually *means* the timezone -3.
+        if res.stdabbr in ("GMT", "UTC") and not posix_offset:
+            res.stdoffset *= -1
+
+        # We must initialize it first, since _delta() needs
+        # _std_offset and _dst_offset set. Use False in start/end
+        # to avoid building it two times.
+        tzrange.__init__(self, res.stdabbr, res.stdoffset,
+                         res.dstabbr, res.dstoffset,
+                         start=False, end=False)
+
+        if not res.dstabbr:
+            self._start_delta = None
+            self._end_delta = None
+        else:
+            self._start_delta = self._delta(res.start)
+            if self._start_delta:
+                self._end_delta = self._delta(res.end, isend=1)
+
+        self.hasdst = bool(self._start_delta)
+
+    def _delta(self, x, isend=0):
+        from dateutil import relativedelta
+        kwargs = {}
+        if x.month is not None:
+            kwargs["month"] = x.month
+            if x.weekday is not None:
+                kwargs["weekday"] = relativedelta.weekday(x.weekday, x.week)
+                if x.week > 0:
+                    kwargs["day"] = 1
+                else:
+                    kwargs["day"] = 31
+            elif x.day:
+                kwargs["day"] = x.day
+        elif x.yday is not None:
+            kwargs["yearday"] = x.yday
+        elif x.jyday is not None:
+            kwargs["nlyearday"] = x.jyday
+        if not kwargs:
+            # Default is to start on first sunday of april, and end
+            # on last sunday of october.
+            if not isend:
+                kwargs["month"] = 4
+                kwargs["day"] = 1
+                kwargs["weekday"] = relativedelta.SU(+1)
+            else:
+                kwargs["month"] = 10
+                kwargs["day"] = 31
+                kwargs["weekday"] = relativedelta.SU(-1)
+        if x.time is not None:
+            kwargs["seconds"] = x.time
+        else:
+            # Default is 2AM.
+            kwargs["seconds"] = 7200
+        if isend:
+            # Convert to standard time, to follow the documented way
+            # of working with the extra hour. See the documentation
+            # of the tzinfo class.
+            delta = self._dst_offset - self._std_offset
+            kwargs["seconds"] -= delta.seconds + delta.days * 86400
+        return relativedelta.relativedelta(**kwargs)
+
+    def __repr__(self):
+        return "%s(%s)" % (self.__class__.__name__, repr(self._s))
+
+
+class _tzicalvtzcomp(object):
+    def __init__(self, tzoffsetfrom, tzoffsetto, isdst,
+                 tzname=None, rrule=None):
+        self.tzoffsetfrom = datetime.timedelta(seconds=tzoffsetfrom)
+        self.tzoffsetto = datetime.timedelta(seconds=tzoffsetto)
+        self.tzoffsetdiff = self.tzoffsetto - self.tzoffsetfrom
+        self.isdst = isdst
+        self.tzname = tzname
+        self.rrule = rrule
+
+
+class _tzicalvtz(_tzinfo):
+    def __init__(self, tzid, comps=[]):
+        super(_tzicalvtz, self).__init__()
+
+        self._tzid = tzid
+        self._comps = comps
+        self._cachedate = []
+        self._cachecomp = []
+        self._cache_lock = _thread.allocate_lock()
+
+    def _find_comp(self, dt):
+        if len(self._comps) == 1:
+            return self._comps[0]
+
+        dt = dt.replace(tzinfo=None)
+
+        try:
+            with self._cache_lock:
+                return self._cachecomp[self._cachedate.index(
+                    (dt, self._fold(dt)))]
+        except ValueError:
+            pass
+
+        lastcompdt = None
+        lastcomp = None
+
+        for comp in self._comps:
+            compdt = self._find_compdt(comp, dt)
+
+            if compdt and (not lastcompdt or lastcompdt < compdt):
+                lastcompdt = compdt
+                lastcomp = comp
+
+        if not lastcomp:
+            # RFC says nothing about what to do when a given
+            # time is before the first onset date. We'll look for the
+            # first standard component, or the first component, if
+            # none is found.
+            for comp in self._comps:
+                if not comp.isdst:
+                    lastcomp = comp
+                    break
+            else:
+                lastcomp = comp[0]
+
+        with self._cache_lock:
+            self._cachedate.insert(0, (dt, self._fold(dt)))
+            self._cachecomp.insert(0, lastcomp)
+
+            if len(self._cachedate) > 10:
+                self._cachedate.pop()
+                self._cachecomp.pop()
+
+        return lastcomp
+
+    def _find_compdt(self, comp, dt):
+        if comp.tzoffsetdiff < ZERO and self._fold(dt):
+            dt -= comp.tzoffsetdiff
+
+        compdt = comp.rrule.before(dt, inc=True)
+
+        return compdt
+
+    def utcoffset(self, dt):
+        if dt is None:
+            return None
+
+        return self._find_comp(dt).tzoffsetto
+
+    def dst(self, dt):
+        comp = self._find_comp(dt)
+        if comp.isdst:
+            return comp.tzoffsetdiff
+        else:
+            return ZERO
+
+    @tzname_in_python2
+    def tzname(self, dt):
+        return self._find_comp(dt).tzname
+
+    def __repr__(self):
+        return "<tzicalvtz %s>" % repr(self._tzid)
+
+    __reduce__ = object.__reduce__
+
+
+class tzical(object):
+    """
+    This object is designed to parse an iCalendar-style ``VTIMEZONE`` structure
+    as set out in `RFC 5545`_ Section 4.6.5 into one or more `tzinfo` objects.
+
+    :param `fileobj`:
+        A file or stream in iCalendar format, which should be UTF-8 encoded
+        with CRLF endings.
+
+    .. _`RFC 5545`: https://tools.ietf.org/html/rfc5545
+    """
+    def __init__(self, fileobj):
+        global rrule
+        from dateutil import rrule
+
+        if isinstance(fileobj, string_types):
+            self._s = fileobj
+            # ical should be encoded in UTF-8 with CRLF
+            fileobj = open(fileobj, 'r')
+        else:
+            self._s = getattr(fileobj, 'name', repr(fileobj))
+            fileobj = _nullcontext(fileobj)
+
+        self._vtz = {}
+
+        with fileobj as fobj:
+            self._parse_rfc(fobj.read())
+
+    def keys(self):
+        """
+        Retrieves the available time zones as a list.
+        """
+        return list(self._vtz.keys())
+
+    def get(self, tzid=None):
+        """
+        Retrieve a :py:class:`datetime.tzinfo` object by its ``tzid``.
+
+        :param tzid:
+            If there is exactly one time zone available, omitting ``tzid``
+            or passing :py:const:`None` value returns it. Otherwise a valid
+            key (which can be retrieved from :func:`keys`) is required.
+
+        :raises ValueError:
+            Raised if ``tzid`` is not specified but there are either more
+            or fewer than 1 zone defined.
+
+        :returns:
+            Returns either a :py:class:`datetime.tzinfo` object representing
+            the relevant time zone or :py:const:`None` if the ``tzid`` was
+            not found.
+        """
+        if tzid is None:
+            if len(self._vtz) == 0:
+                raise ValueError("no timezones defined")
+            elif len(self._vtz) > 1:
+                raise ValueError("more than one timezone available")
+            tzid = next(iter(self._vtz))
+
+        return self._vtz.get(tzid)
+
+    def _parse_offset(self, s):
+        s = s.strip()
+        if not s:
+            raise ValueError("empty offset")
+        if s[0] in ('+', '-'):
+            signal = (-1, +1)[s[0] == '+']
+            s = s[1:]
+        else:
+            signal = +1
+        if len(s) == 4:
+            return (int(s[:2]) * 3600 + int(s[2:]) * 60) * signal
+        elif len(s) == 6:
+            return (int(s[:2]) * 3600 + int(s[2:4]) * 60 + int(s[4:])) * signal
+        else:
+            raise ValueError("invalid offset: " + s)
+
+    def _parse_rfc(self, s):
+        lines = s.splitlines()
+        if not lines:
+            raise ValueError("empty string")
+
+        # Unfold
+        i = 0
+        while i < len(lines):
+            line = lines[i].rstrip()
+            if not line:
+                del lines[i]
+            elif i > 0 and line[0] == " ":
+                lines[i-1] += line[1:]
+                del lines[i]
+            else:
+                i += 1
+
+        tzid = None
+        comps = []
+        invtz = False
+        comptype = None
+        for line in lines:
+            if not line:
+                continue
+            name, value = line.split(':', 1)
+            parms = name.split(';')
+            if not parms:
+                raise ValueError("empty property name")
+            name = parms[0].upper()
+            parms = parms[1:]
+            if invtz:
+                if name == "BEGIN":
+                    if value in ("STANDARD", "DAYLIGHT"):
+                        # Process component
+                        pass
+                    else:
+                        raise ValueError("unknown component: "+value)
+                    comptype = value
+                    founddtstart = False
+                    tzoffsetfrom = None
+                    tzoffsetto = None
+                    rrulelines = []
+                    tzname = None
+                elif name == "END":
+                    if value == "VTIMEZONE":
+                        if comptype:
+                            raise ValueError("component not closed: "+comptype)
+                        if not tzid:
+                            raise ValueError("mandatory TZID not found")
+                        if not comps:
+                            raise ValueError(
+                                "at least one component is needed")
+                        # Process vtimezone
+                        self._vtz[tzid] = _tzicalvtz(tzid, comps)
+                        invtz = False
+                    elif value == comptype:
+                        if not founddtstart:
+                            raise ValueError("mandatory DTSTART not found")
+                        if tzoffsetfrom is None:
+                            raise ValueError(
+                                "mandatory TZOFFSETFROM not found")
+                        if tzoffsetto is None:
+                            raise ValueError(
+                                "mandatory TZOFFSETFROM not found")
+                        # Process component
+                        rr = None
+                        if rrulelines:
+                            rr = rrule.rrulestr("\n".join(rrulelines),
+                                                compatible=True,
+                                                ignoretz=True,
+                                                cache=True)
+                        comp = _tzicalvtzcomp(tzoffsetfrom, tzoffsetto,
+                                              (comptype == "DAYLIGHT"),
+                                              tzname, rr)
+                        comps.append(comp)
+                        comptype = None
+                    else:
+                        raise ValueError("invalid component end: "+value)
+                elif comptype:
+                    if name == "DTSTART":
+                        # DTSTART in VTIMEZONE takes a subset of valid RRULE
+                        # values under RFC 5545.
+                        for parm in parms:
+                            if parm != 'VALUE=DATE-TIME':
+                                msg = ('Unsupported DTSTART param in ' +
+                                       'VTIMEZONE: ' + parm)
+                                raise ValueError(msg)
+                        rrulelines.append(line)
+                        founddtstart = True
+                    elif name in ("RRULE", "RDATE", "EXRULE", "EXDATE"):
+                        rrulelines.append(line)
+                    elif name == "TZOFFSETFROM":
+                        if parms:
+                            raise ValueError(
+                                "unsupported %s parm: %s " % (name, parms[0]))
+                        tzoffsetfrom = self._parse_offset(value)
+                    elif name == "TZOFFSETTO":
+                        if parms:
+                            raise ValueError(
+                                "unsupported TZOFFSETTO parm: "+parms[0])
+                        tzoffsetto = self._parse_offset(value)
+                    elif name == "TZNAME":
+                        if parms:
+                            raise ValueError(
+                                "unsupported TZNAME parm: "+parms[0])
+                        tzname = value
+                    elif name == "COMMENT":
+                        pass
+                    else:
+                        raise ValueError("unsupported property: "+name)
+                else:
+                    if name == "TZID":
+                        if parms:
+                            raise ValueError(
+                                "unsupported TZID parm: "+parms[0])
+                        tzid = value
+                    elif name in ("TZURL", "LAST-MODIFIED", "COMMENT"):
+                        pass
+                    else:
+                        raise ValueError("unsupported property: "+name)
+            elif name == "BEGIN" and value == "VTIMEZONE":
+                tzid = None
+                comps = []
+                invtz = True
+
+    def __repr__(self):
+        return "%s(%s)" % (self.__class__.__name__, repr(self._s))
+
+
+if sys.platform != "win32":
+    TZFILES = ["/etc/localtime", "localtime"]
+    TZPATHS = ["/usr/share/zoneinfo",
+               "/usr/lib/zoneinfo",
+               "/usr/share/lib/zoneinfo",
+               "/etc/zoneinfo"]
+else:
+    TZFILES = []
+    TZPATHS = []
+
+
+def __get_gettz():
+    tzlocal_classes = (tzlocal,)
+    if tzwinlocal is not None:
+        tzlocal_classes += (tzwinlocal,)
+
+    class GettzFunc(object):
+        """
+        Retrieve a time zone object from a string representation
+
+        This function is intended to retrieve the :py:class:`tzinfo` subclass
+        that best represents the time zone that would be used if a POSIX
+        `TZ variable`_ were set to the same value.
+
+        If no argument or an empty string is passed to ``gettz``, local time
+        is returned:
+
+        .. code-block:: python3
+
+            >>> gettz()
+            tzfile('/etc/localtime')
+
+        This function is also the preferred way to map IANA tz database keys
+        to :class:`tzfile` objects:
+
+        .. code-block:: python3
+
+            >>> gettz('Pacific/Kiritimati')
+            tzfile('/usr/share/zoneinfo/Pacific/Kiritimati')
+
+        On Windows, the standard is extended to include the Windows-specific
+        zone names provided by the operating system:
+
+        .. code-block:: python3
+
+            >>> gettz('Egypt Standard Time')
+            tzwin('Egypt Standard Time')
+
+        Passing a GNU ``TZ`` style string time zone specification returns a
+        :class:`tzstr` object:
+
+        .. code-block:: python3
+
+            >>> gettz('AEST-10AEDT-11,M10.1.0/2,M4.1.0/3')
+            tzstr('AEST-10AEDT-11,M10.1.0/2,M4.1.0/3')
+
+        :param name:
+            A time zone name (IANA, or, on Windows, Windows keys), location of
+            a ``tzfile(5)`` zoneinfo file or ``TZ`` variable style time zone
+            specifier. An empty string, no argument or ``None`` is interpreted
+            as local time.
+
+        :return:
+            Returns an instance of one of ``dateutil``'s :py:class:`tzinfo`
+            subclasses.
+
+        .. versionchanged:: 2.7.0
+
+            After version 2.7.0, any two calls to ``gettz`` using the same
+            input strings will return the same object:
+
+            .. code-block:: python3
+
+                >>> tz.gettz('America/Chicago') is tz.gettz('America/Chicago')
+                True
+
+            In addition to improving performance, this ensures that
+            `"same zone" semantics`_ are used for datetimes in the same zone.
+
+
+        .. _`TZ variable`:
+            https://www.gnu.org/software/libc/manual/html_node/TZ-Variable.html
+
+        .. _`"same zone" semantics`:
+            https://blog.ganssle.io/articles/2018/02/aware-datetime-arithmetic.html
+        """
+        def __init__(self):
+
+            self.__instances = weakref.WeakValueDictionary()
+            self.__strong_cache_size = 8
+            self.__strong_cache = OrderedDict()
+            self._cache_lock = _thread.allocate_lock()
+
+        def __call__(self, name=None):
+            with self._cache_lock:
+                rv = self.__instances.get(name, None)
+
+                if rv is None:
+                    rv = self.nocache(name=name)
+                    if not (name is None
+                            or isinstance(rv, tzlocal_classes)
+                            or rv is None):
+                        # tzlocal is slightly more complicated than the other
+                        # time zone providers because it depends on environment
+                        # at construction time, so don't cache that.
+                        #
+                        # We also cannot store weak references to None, so we
+                        # will also not store that.
+                        self.__instances[name] = rv
+                    else:
+                        # No need for strong caching, return immediately
+                        return rv
+
+                self.__strong_cache[name] = self.__strong_cache.pop(name, rv)
+
+                if len(self.__strong_cache) > self.__strong_cache_size:
+                    self.__strong_cache.popitem(last=False)
+
+            return rv
+
+        def set_cache_size(self, size):
+            with self._cache_lock:
+                self.__strong_cache_size = size
+                while len(self.__strong_cache) > size:
+                    self.__strong_cache.popitem(last=False)
+
+        def cache_clear(self):
+            with self._cache_lock:
+                self.__instances = weakref.WeakValueDictionary()
+                self.__strong_cache.clear()
+
+        @staticmethod
+        def nocache(name=None):
+            """A non-cached version of gettz"""
+            tz = None
+            if not name:
+                try:
+                    name = os.environ["TZ"]
+                except KeyError:
+                    pass
+            if name is None or name in ("", ":"):
+                for filepath in TZFILES:
+                    if not os.path.isabs(filepath):
+                        filename = filepath
+                        for path in TZPATHS:
+                            filepath = os.path.join(path, filename)
+                            if os.path.isfile(filepath):
+                                break
+                        else:
+                            continue
+                    if os.path.isfile(filepath):
+                        try:
+                            tz = tzfile(filepath)
+                            break
+                        except (IOError, OSError, ValueError):
+                            pass
+                else:
+                    tz = tzlocal()
+            else:
+                try:
+                    if name.startswith(":"):
+                        name = name[1:]
+                except TypeError as e:
+                    if isinstance(name, bytes):
+                        new_msg = "gettz argument should be str, not bytes"
+                        six.raise_from(TypeError(new_msg), e)
+                    else:
+                        raise
+                if os.path.isabs(name):
+                    if os.path.isfile(name):
+                        tz = tzfile(name)
+                    else:
+                        tz = None
+                else:
+                    for path in TZPATHS:
+                        filepath = os.path.join(path, name)
+                        if not os.path.isfile(filepath):
+                            filepath = filepath.replace(' ', '_')
+                            if not os.path.isfile(filepath):
+                                continue
+                        try:
+                            tz = tzfile(filepath)
+                            break
+                        except (IOError, OSError, ValueError):
+                            pass
+                    else:
+                        tz = None
+                        if tzwin is not None:
+                            try:
+                                tz = tzwin(name)
+                            except (WindowsError, UnicodeEncodeError):
+                                # UnicodeEncodeError is for Python 2.7 compat
+                                tz = None
+
+                        if not tz:
+                            from dateutil.zoneinfo import get_zonefile_instance
+                            tz = get_zonefile_instance().get(name)
+
+                        if not tz:
+                            for c in name:
+                                # name is not a tzstr unless it has at least
+                                # one offset. For short values of "name", an
+                                # explicit for loop seems to be the fastest way
+                                # To determine if a string contains a digit
+                                if c in "0123456789":
+                                    try:
+                                        tz = tzstr(name)
+                                    except ValueError:
+                                        pass
+                                    break
+                            else:
+                                if name in ("GMT", "UTC"):
+                                    tz = UTC
+                                elif name in time.tzname:
+                                    tz = tzlocal()
+            return tz
+
+    return GettzFunc()
+
+
+gettz = __get_gettz()
+del __get_gettz
+
+
+def datetime_exists(dt, tz=None):
+    """
+    Given a datetime and a time zone, determine whether or not a given datetime
+    would fall in a gap.
+
+    :param dt:
+        A :class:`datetime.datetime` (whose time zone will be ignored if ``tz``
+        is provided.)
+
+    :param tz:
+        A :class:`datetime.tzinfo` with support for the ``fold`` attribute. If
+        ``None`` or not provided, the datetime's own time zone will be used.
+
+    :return:
+        Returns a boolean value whether or not the "wall time" exists in
+        ``tz``.
+
+    .. versionadded:: 2.7.0
+    """
+    if tz is None:
+        if dt.tzinfo is None:
+            raise ValueError('Datetime is naive and no time zone provided.')
+        tz = dt.tzinfo
+
+    dt = dt.replace(tzinfo=None)
+
+    # This is essentially a test of whether or not the datetime can survive
+    # a round trip to UTC.
+    dt_rt = dt.replace(tzinfo=tz).astimezone(UTC).astimezone(tz)
+    dt_rt = dt_rt.replace(tzinfo=None)
+
+    return dt == dt_rt
+
+
+def datetime_ambiguous(dt, tz=None):
+    """
+    Given a datetime and a time zone, determine whether or not a given datetime
+    is ambiguous (i.e if there are two times differentiated only by their DST
+    status).
+
+    :param dt:
+        A :class:`datetime.datetime` (whose time zone will be ignored if ``tz``
+        is provided.)
+
+    :param tz:
+        A :class:`datetime.tzinfo` with support for the ``fold`` attribute. If
+        ``None`` or not provided, the datetime's own time zone will be used.
+
+    :return:
+        Returns a boolean value whether or not the "wall time" is ambiguous in
+        ``tz``.
+
+    .. versionadded:: 2.6.0
+    """
+    if tz is None:
+        if dt.tzinfo is None:
+            raise ValueError('Datetime is naive and no time zone provided.')
+
+        tz = dt.tzinfo
+
+    # If a time zone defines its own "is_ambiguous" function, we'll use that.
+    is_ambiguous_fn = getattr(tz, 'is_ambiguous', None)
+    if is_ambiguous_fn is not None:
+        try:
+            return tz.is_ambiguous(dt)
+        except Exception:
+            pass
+
+    # If it doesn't come out and tell us it's ambiguous, we'll just check if
+    # the fold attribute has any effect on this particular date and time.
+    dt = dt.replace(tzinfo=tz)
+    wall_0 = enfold(dt, fold=0)
+    wall_1 = enfold(dt, fold=1)
+
+    same_offset = wall_0.utcoffset() == wall_1.utcoffset()
+    same_dst = wall_0.dst() == wall_1.dst()
+
+    return not (same_offset and same_dst)
+
+
+def resolve_imaginary(dt):
+    """
+    Given a datetime that may be imaginary, return an existing datetime.
+
+    This function assumes that an imaginary datetime represents what the
+    wall time would be in a zone had the offset transition not occurred, so
+    it will always fall forward by the transition's change in offset.
+
+    .. doctest::
+
+        >>> from dateutil import tz
+        >>> from datetime import datetime
+        >>> NYC = tz.gettz('America/New_York')
+        >>> print(tz.resolve_imaginary(datetime(2017, 3, 12, 2, 30, tzinfo=NYC)))
+        2017-03-12 03:30:00-04:00
+
+        >>> KIR = tz.gettz('Pacific/Kiritimati')
+        >>> print(tz.resolve_imaginary(datetime(1995, 1, 1, 12, 30, tzinfo=KIR)))
+        1995-01-02 12:30:00+14:00
+
+    As a note, :func:`datetime.astimezone` is guaranteed to produce a valid,
+    existing datetime, so a round-trip to and from UTC is sufficient to get
+    an extant datetime, however, this generally "falls back" to an earlier time
+    rather than falling forward to the STD side (though no guarantees are made
+    about this behavior).
+
+    :param dt:
+        A :class:`datetime.datetime` which may or may not exist.
+
+    :return:
+        Returns an existing :class:`datetime.datetime`. If ``dt`` was not
+        imaginary, the datetime returned is guaranteed to be the same object
+        passed to the function.
+
+    .. versionadded:: 2.7.0
+    """
+    if dt.tzinfo is not None and not datetime_exists(dt):
+
+        curr_offset = (dt + datetime.timedelta(hours=24)).utcoffset()
+        old_offset = (dt - datetime.timedelta(hours=24)).utcoffset()
+
+        dt += curr_offset - old_offset
+
+    return dt
+
+
+def _datetime_to_timestamp(dt):
+    """
+    Convert a :class:`datetime.datetime` object to an epoch timestamp in
+    seconds since January 1, 1970, ignoring the time zone.
+    """
+    return (dt.replace(tzinfo=None) - EPOCH).total_seconds()
+
+
+if sys.version_info >= (3, 6):
+    def _get_supported_offset(second_offset):
+        return second_offset
+else:
+    def _get_supported_offset(second_offset):
+        # For python pre-3.6, round to full-minutes if that's not the case.
+        # Python's datetime doesn't accept sub-minute timezones. Check
+        # http://python.org/sf/1447945 or https://bugs.python.org/issue5288
+        # for some information.
+        old_offset = second_offset
+        calculated_offset = 60 * ((second_offset + 30) // 60)
+        return calculated_offset
+
+
+try:
+    # Python 3.7 feature
+    from contextlib import nullcontext as _nullcontext
+except ImportError:
+    class _nullcontext(object):
+        """
+        Class for wrapping contexts so that they are passed through in a
+        with statement.
+        """
+        def __init__(self, context):
+            self.context = context
+
+        def __enter__(self):
+            return self.context
+
+        def __exit__(*args, **kwargs):
+            pass
+
+# vim:ts=4:sw=4:et

venv/lib/python3.10/site-packages/dateutil/tz/win.py

@@ -0,0 +1,370 @@
+# -*- coding: utf-8 -*-
+"""
+This module provides an interface to the native time zone data on Windows,
+including :py:class:`datetime.tzinfo` implementations.
+
+Attempting to import this module on a non-Windows platform will raise an
+:py:obj:`ImportError`.
+"""
+# This code was originally contributed by Jeffrey Harris.
+import datetime
+import struct
+
+from six.moves import winreg
+from six import text_type
+
+try:
+    import ctypes
+    from ctypes import wintypes
+except ValueError:
+    # ValueError is raised on non-Windows systems for some horrible reason.
+    raise ImportError("Running tzwin on non-Windows system")
+
+from ._common import tzrangebase
+
+__all__ = ["tzwin", "tzwinlocal", "tzres"]
+
+ONEWEEK = datetime.timedelta(7)
+
+TZKEYNAMENT = r"SOFTWARE\Microsoft\Windows NT\CurrentVersion\Time Zones"
+TZKEYNAME9X = r"SOFTWARE\Microsoft\Windows\CurrentVersion\Time Zones"
+TZLOCALKEYNAME = r"SYSTEM\CurrentControlSet\Control\TimeZoneInformation"
+
+
+def _settzkeyname():
+    handle = winreg.ConnectRegistry(None, winreg.HKEY_LOCAL_MACHINE)
+    try:
+        winreg.OpenKey(handle, TZKEYNAMENT).Close()
+        TZKEYNAME = TZKEYNAMENT
+    except WindowsError:
+        TZKEYNAME = TZKEYNAME9X
+    handle.Close()
+    return TZKEYNAME
+
+
+TZKEYNAME = _settzkeyname()
+
+
+class tzres(object):
+    """
+    Class for accessing ``tzres.dll``, which contains timezone name related
+    resources.
+
+    .. versionadded:: 2.5.0
+    """
+    p_wchar = ctypes.POINTER(wintypes.WCHAR)        # Pointer to a wide char
+
+    def __init__(self, tzres_loc='tzres.dll'):
+        # Load the user32 DLL so we can load strings from tzres
+        user32 = ctypes.WinDLL('user32')
+
+        # Specify the LoadStringW function
+        user32.LoadStringW.argtypes = (wintypes.HINSTANCE,
+                                       wintypes.UINT,
+                                       wintypes.LPWSTR,
+                                       ctypes.c_int)
+
+        self.LoadStringW = user32.LoadStringW
+        self._tzres = ctypes.WinDLL(tzres_loc)
+        self.tzres_loc = tzres_loc
+
+    def load_name(self, offset):
+        """
+        Load a timezone name from a DLL offset (integer).
+
+        >>> from dateutil.tzwin import tzres
+        >>> tzr = tzres()
+        >>> print(tzr.load_name(112))
+        'Eastern Standard Time'
+
+        :param offset:
+            A positive integer value referring to a string from the tzres dll.
+
+        .. note::
+
+            Offsets found in the registry are generally of the form
+            ``@tzres.dll,-114``. The offset in this case is 114, not -114.
+
+        """
+        resource = self.p_wchar()
+        lpBuffer = ctypes.cast(ctypes.byref(resource), wintypes.LPWSTR)
+        nchar = self.LoadStringW(self._tzres._handle, offset, lpBuffer, 0)
+        return resource[:nchar]
+
+    def name_from_string(self, tzname_str):
+        """
+        Parse strings as returned from the Windows registry into the time zone
+        name as defined in the registry.
+
+        >>> from dateutil.tzwin import tzres
+        >>> tzr = tzres()
+        >>> print(tzr.name_from_string('@tzres.dll,-251'))
+        'Dateline Daylight Time'
+        >>> print(tzr.name_from_string('Eastern Standard Time'))
+        'Eastern Standard Time'
+
+        :param tzname_str:
+            A timezone name string as returned from a Windows registry key.
+
+        :return:
+            Returns the localized timezone string from tzres.dll if the string
+            is of the form `@tzres.dll,-offset`, else returns the input string.
+        """
+        if not tzname_str.startswith('@'):
+            return tzname_str
+
+        name_splt = tzname_str.split(',-')
+        try:
+            offset = int(name_splt[1])
+        except:
+            raise ValueError("Malformed timezone string.")
+
+        return self.load_name(offset)
+
+
+class tzwinbase(tzrangebase):
+    """tzinfo class based on win32's timezones available in the registry."""
+    def __init__(self):
+        raise NotImplementedError('tzwinbase is an abstract base class')
+
+    def __eq__(self, other):
+        # Compare on all relevant dimensions, including name.
+        if not isinstance(other, tzwinbase):
+            return NotImplemented
+
+        return  (self._std_offset == other._std_offset and
+                 self._dst_offset == other._dst_offset and
+                 self._stddayofweek == other._stddayofweek and
+                 self._dstdayofweek == other._dstdayofweek and
+                 self._stdweeknumber == other._stdweeknumber and
+                 self._dstweeknumber == other._dstweeknumber and
+                 self._stdhour == other._stdhour and
+                 self._dsthour == other._dsthour and
+                 self._stdminute == other._stdminute and
+                 self._dstminute == other._dstminute and
+                 self._std_abbr == other._std_abbr and
+                 self._dst_abbr == other._dst_abbr)
+
+    @staticmethod
+    def list():
+        """Return a list of all time zones known to the system."""
+        with winreg.ConnectRegistry(None, winreg.HKEY_LOCAL_MACHINE) as handle:
+            with winreg.OpenKey(handle, TZKEYNAME) as tzkey:
+                result = [winreg.EnumKey(tzkey, i)
+                          for i in range(winreg.QueryInfoKey(tzkey)[0])]
+        return result
+
+    def display(self):
+        """
+        Return the display name of the time zone.
+        """
+        return self._display
+
+    def transitions(self, year):
+        """
+        For a given year, get the DST on and off transition times, expressed
+        always on the standard time side. For zones with no transitions, this
+        function returns ``None``.
+
+        :param year:
+            The year whose transitions you would like to query.
+
+        :return:
+            Returns a :class:`tuple` of :class:`datetime.datetime` objects,
+            ``(dston, dstoff)`` for zones with an annual DST transition, or
+            ``None`` for fixed offset zones.
+        """
+
+        if not self.hasdst:
+            return None
+
+        dston = picknthweekday(year, self._dstmonth, self._dstdayofweek,
+                               self._dsthour, self._dstminute,
+                               self._dstweeknumber)
+
+        dstoff = picknthweekday(year, self._stdmonth, self._stddayofweek,
+                                self._stdhour, self._stdminute,
+                                self._stdweeknumber)
+
+        # Ambiguous dates default to the STD side
+        dstoff -= self._dst_base_offset
+
+        return dston, dstoff
+
+    def _get_hasdst(self):
+        return self._dstmonth != 0
+
+    @property
+    def _dst_base_offset(self):
+        return self._dst_base_offset_
+
+
+class tzwin(tzwinbase):
+    """
+    Time zone object created from the zone info in the Windows registry
+
+    These are similar to :py:class:`dateutil.tz.tzrange` objects in that
+    the time zone data is provided in the format of a single offset rule
+    for either 0 or 2 time zone transitions per year.
+
+    :param: name
+        The name of a Windows time zone key, e.g. "Eastern Standard Time".
+        The full list of keys can be retrieved with :func:`tzwin.list`.
+    """
+
+    def __init__(self, name):
+        self._name = name
+
+        with winreg.ConnectRegistry(None, winreg.HKEY_LOCAL_MACHINE) as handle:
+            tzkeyname = text_type("{kn}\\{name}").format(kn=TZKEYNAME, name=name)
+            with winreg.OpenKey(handle, tzkeyname) as tzkey:
+                keydict = valuestodict(tzkey)
+
+        self._std_abbr = keydict["Std"]
+        self._dst_abbr = keydict["Dlt"]
+
+        self._display = keydict["Display"]
+
+        # See http://ww_winreg.jsiinc.com/SUBA/tip0300/rh0398.htm
+        tup = struct.unpack("=3l16h", keydict["TZI"])
+        stdoffset = -tup[0]-tup[1]          # Bias + StandardBias * -1
+        dstoffset = stdoffset-tup[2]        # + DaylightBias * -1
+        self._std_offset = datetime.timedelta(minutes=stdoffset)
+        self._dst_offset = datetime.timedelta(minutes=dstoffset)
+
+        # for the meaning see the win32 TIME_ZONE_INFORMATION structure docs
+        # http://msdn.microsoft.com/en-us/library/windows/desktop/ms725481(v=vs.85).aspx
+        (self._stdmonth,
+         self._stddayofweek,   # Sunday = 0
+         self._stdweeknumber,  # Last = 5
+         self._stdhour,
+         self._stdminute) = tup[4:9]
+
+        (self._dstmonth,
+         self._dstdayofweek,   # Sunday = 0
+         self._dstweeknumber,  # Last = 5
+         self._dsthour,
+         self._dstminute) = tup[12:17]
+
+        self._dst_base_offset_ = self._dst_offset - self._std_offset
+        self.hasdst = self._get_hasdst()
+
+    def __repr__(self):
+        return "tzwin(%s)" % repr(self._name)
+
+    def __reduce__(self):
+        return (self.__class__, (self._name,))
+
+
+class tzwinlocal(tzwinbase):
+    """
+    Class representing the local time zone information in the Windows registry
+
+    While :class:`dateutil.tz.tzlocal` makes system calls (via the :mod:`time`
+    module) to retrieve time zone information, ``tzwinlocal`` retrieves the
+    rules directly from the Windows registry and creates an object like
+    :class:`dateutil.tz.tzwin`.
+
+    Because Windows does not have an equivalent of :func:`time.tzset`, on
+    Windows, :class:`dateutil.tz.tzlocal` instances will always reflect the
+    time zone settings *at the time that the process was started*, meaning
+    changes to the machine's time zone settings during the run of a program
+    on Windows will **not** be reflected by :class:`dateutil.tz.tzlocal`.
+    Because ``tzwinlocal`` reads the registry directly, it is unaffected by
+    this issue.
+    """
+    def __init__(self):
+        with winreg.ConnectRegistry(None, winreg.HKEY_LOCAL_MACHINE) as handle:
+            with winreg.OpenKey(handle, TZLOCALKEYNAME) as tzlocalkey:
+                keydict = valuestodict(tzlocalkey)
+
+            self._std_abbr = keydict["StandardName"]
+            self._dst_abbr = keydict["DaylightName"]
+
+            try:
+                tzkeyname = text_type('{kn}\\{sn}').format(kn=TZKEYNAME,
+                                                          sn=self._std_abbr)
+                with winreg.OpenKey(handle, tzkeyname) as tzkey:
+                    _keydict = valuestodict(tzkey)
+                    self._display = _keydict["Display"]
+            except OSError:
+                self._display = None
+
+        stdoffset = -keydict["Bias"]-keydict["StandardBias"]
+        dstoffset = stdoffset-keydict["DaylightBias"]
+
+        self._std_offset = datetime.timedelta(minutes=stdoffset)
+        self._dst_offset = datetime.timedelta(minutes=dstoffset)
+
+        # For reasons unclear, in this particular key, the day of week has been
+        # moved to the END of the SYSTEMTIME structure.
+        tup = struct.unpack("=8h", keydict["StandardStart"])
+
+        (self._stdmonth,
+         self._stdweeknumber,  # Last = 5
+         self._stdhour,
+         self._stdminute) = tup[1:5]
+
+        self._stddayofweek = tup[7]
+
+        tup = struct.unpack("=8h", keydict["DaylightStart"])
+
+        (self._dstmonth,
+         self._dstweeknumber,  # Last = 5
+         self._dsthour,
+         self._dstminute) = tup[1:5]
+
+        self._dstdayofweek = tup[7]
+
+        self._dst_base_offset_ = self._dst_offset - self._std_offset
+        self.hasdst = self._get_hasdst()
+
+    def __repr__(self):
+        return "tzwinlocal()"
+
+    def __str__(self):
+        # str will return the standard name, not the daylight name.
+        return "tzwinlocal(%s)" % repr(self._std_abbr)
+
+    def __reduce__(self):
+        return (self.__class__, ())
+
+
+def picknthweekday(year, month, dayofweek, hour, minute, whichweek):
+    """ dayofweek == 0 means Sunday, whichweek 5 means last instance """
+    first = datetime.datetime(year, month, 1, hour, minute)
+
+    # This will work if dayofweek is ISO weekday (1-7) or Microsoft-style (0-6),
+    # Because 7 % 7 = 0
+    weekdayone = first.replace(day=((dayofweek - first.isoweekday()) % 7) + 1)
+    wd = weekdayone + ((whichweek - 1) * ONEWEEK)
+    if (wd.month != month):
+        wd -= ONEWEEK
+
+    return wd
+
+
+def valuestodict(key):
+    """Convert a registry key's values to a dictionary."""
+    dout = {}
+    size = winreg.QueryInfoKey(key)[1]
+    tz_res = None
+
+    for i in range(size):
+        key_name, value, dtype = winreg.EnumValue(key, i)
+        if dtype == winreg.REG_DWORD or dtype == winreg.REG_DWORD_LITTLE_ENDIAN:
+            # If it's a DWORD (32-bit integer), it's stored as unsigned - convert
+            # that to a proper signed integer
+            if value & (1 << 31):
+                value = value - (1 << 32)
+        elif dtype == winreg.REG_SZ:
+            # If it's a reference to the tzres DLL, load the actual string
+            if value.startswith('@tzres'):
+                tz_res = tz_res or tzres()
+                value = tz_res.name_from_string(value)
+
+            value = value.rstrip('\x00')    # Remove trailing nulls
+
+        dout[key_name] = value
+
+    return dout

venv/lib/python3.10/site-packages/dateutil/zoneinfo/__init__.py

@@ -0,0 +1,167 @@
+# -*- coding: utf-8 -*-
+import warnings
+import json
+
+from tarfile import TarFile
+from pkgutil import get_data
+from io import BytesIO
+
+from dateutil.tz import tzfile as _tzfile
+
+__all__ = ["get_zonefile_instance", "gettz", "gettz_db_metadata"]
+
+ZONEFILENAME = "dateutil-zoneinfo.tar.gz"
+METADATA_FN = 'METADATA'
+
+
+class tzfile(_tzfile):
+    def __reduce__(self):
+        return (gettz, (self._filename,))
+
+
+def getzoneinfofile_stream():
+    try:
+        return BytesIO(get_data(__name__, ZONEFILENAME))
+    except IOError as e:  # TODO  switch to FileNotFoundError?
+        warnings.warn("I/O error({0}): {1}".format(e.errno, e.strerror))
+        return None
+
+
+class ZoneInfoFile(object):
+    def __init__(self, zonefile_stream=None):
+        if zonefile_stream is not None:
+            with TarFile.open(fileobj=zonefile_stream) as tf:
+                self.zones = {zf.name: tzfile(tf.extractfile(zf), filename=zf.name)
+                              for zf in tf.getmembers()
+                              if zf.isfile() and zf.name != METADATA_FN}
+                # deal with links: They'll point to their parent object. Less
+                # waste of memory
+                links = {zl.name: self.zones[zl.linkname]
+                         for zl in tf.getmembers() if
+                         zl.islnk() or zl.issym()}
+                self.zones.update(links)
+                try:
+                    metadata_json = tf.extractfile(tf.getmember(METADATA_FN))
+                    metadata_str = metadata_json.read().decode('UTF-8')
+                    self.metadata = json.loads(metadata_str)
+                except KeyError:
+                    # no metadata in tar file
+                    self.metadata = None
+        else:
+            self.zones = {}
+            self.metadata = None
+
+    def get(self, name, default=None):
+        """
+        Wrapper for :func:`ZoneInfoFile.zones.get`. This is a convenience method
+        for retrieving zones from the zone dictionary.
+
+        :param name:
+            The name of the zone to retrieve. (Generally IANA zone names)
+
+        :param default:
+            The value to return in the event of a missing key.
+
+        .. versionadded:: 2.6.0
+
+        """
+        return self.zones.get(name, default)
+
+
+# The current API has gettz as a module function, although in fact it taps into
+# a stateful class. So as a workaround for now, without changing the API, we
+# will create a new "global" class instance the first time a user requests a
+# timezone. Ugly, but adheres to the api.
+#
+# TODO: Remove after deprecation period.
+_CLASS_ZONE_INSTANCE = []
+
+
+def get_zonefile_instance(new_instance=False):
+    """
+    This is a convenience function which provides a :class:`ZoneInfoFile`
+    instance using the data provided by the ``dateutil`` package. By default, it
+    caches a single instance of the ZoneInfoFile object and returns that.
+
+    :param new_instance:
+        If ``True``, a new instance of :class:`ZoneInfoFile` is instantiated and
+        used as the cached instance for the next call. Otherwise, new instances
+        are created only as necessary.
+
+    :return:
+        Returns a :class:`ZoneInfoFile` object.
+
+    .. versionadded:: 2.6
+    """
+    if new_instance:
+        zif = None
+    else:
+        zif = getattr(get_zonefile_instance, '_cached_instance', None)
+
+    if zif is None:
+        zif = ZoneInfoFile(getzoneinfofile_stream())
+
+        get_zonefile_instance._cached_instance = zif
+
+    return zif
+
+
+def gettz(name):
+    """
+    This retrieves a time zone from the local zoneinfo tarball that is packaged
+    with dateutil.
+
+    :param name:
+        An IANA-style time zone name, as found in the zoneinfo file.
+
+    :return:
+        Returns a :class:`dateutil.tz.tzfile` time zone object.
+
+    .. warning::
+        It is generally inadvisable to use this function, and it is only
+        provided for API compatibility with earlier versions. This is *not*
+        equivalent to ``dateutil.tz.gettz()``, which selects an appropriate
+        time zone based on the inputs, favoring system zoneinfo. This is ONLY
+        for accessing the dateutil-specific zoneinfo (which may be out of
+        date compared to the system zoneinfo).
+
+    .. deprecated:: 2.6
+        If you need to use a specific zoneinfofile over the system zoneinfo,
+        instantiate a :class:`dateutil.zoneinfo.ZoneInfoFile` object and call
+        :func:`dateutil.zoneinfo.ZoneInfoFile.get(name)` instead.
+
+        Use :func:`get_zonefile_instance` to retrieve an instance of the
+        dateutil-provided zoneinfo.
+    """
+    warnings.warn("zoneinfo.gettz() will be removed in future versions, "
+                  "to use the dateutil-provided zoneinfo files, instantiate a "
+                  "ZoneInfoFile object and use ZoneInfoFile.zones.get() "
+                  "instead. See the documentation for details.",
+                  DeprecationWarning)
+
+    if len(_CLASS_ZONE_INSTANCE) == 0:
+        _CLASS_ZONE_INSTANCE.append(ZoneInfoFile(getzoneinfofile_stream()))
+    return _CLASS_ZONE_INSTANCE[0].zones.get(name)
+
+
+def gettz_db_metadata():
+    """ Get the zonefile metadata
+
+    See `zonefile_metadata`_
+
+    :returns:
+        A dictionary with the database metadata
+
+    .. deprecated:: 2.6
+        See deprecation warning in :func:`zoneinfo.gettz`. To get metadata,
+        query the attribute ``zoneinfo.ZoneInfoFile.metadata``.
+    """
+    warnings.warn("zoneinfo.gettz_db_metadata() will be removed in future "
+                  "versions, to use the dateutil-provided zoneinfo files, "
+                  "ZoneInfoFile object and query the 'metadata' attribute "
+                  "instead. See the documentation for details.",
+                  DeprecationWarning)
+
+    if len(_CLASS_ZONE_INSTANCE) == 0:
+        _CLASS_ZONE_INSTANCE.append(ZoneInfoFile(getzoneinfofile_stream()))
+    return _CLASS_ZONE_INSTANCE[0].metadata

venv/lib/python3.10/site-packages/dateutil/zoneinfo/rebuild.py

@@ -0,0 +1,75 @@
+import logging
+import os
+import tempfile
+import shutil
+import json
+from subprocess import check_call, check_output
+from tarfile import TarFile
+
+from dateutil.zoneinfo import METADATA_FN, ZONEFILENAME
+
+
+def rebuild(filename, tag=None, format="gz", zonegroups=[], metadata=None):
+    """Rebuild the internal timezone info in dateutil/zoneinfo/zoneinfo*tar*
+
+    filename is the timezone tarball from ``ftp.iana.org/tz``.
+
+    """
+    tmpdir = tempfile.mkdtemp()
+    zonedir = os.path.join(tmpdir, "zoneinfo")
+    moduledir = os.path.dirname(__file__)
+    try:
+        with TarFile.open(filename) as tf:
+            for name in zonegroups:
+                tf.extract(name, tmpdir)
+            filepaths = [os.path.join(tmpdir, n) for n in zonegroups]
+
+            _run_zic(zonedir, filepaths)
+
+        # write metadata file
+        with open(os.path.join(zonedir, METADATA_FN), 'w') as f:
+            json.dump(metadata, f, indent=4, sort_keys=True)
+        target = os.path.join(moduledir, ZONEFILENAME)
+        with TarFile.open(target, "w:%s" % format) as tf:
+            for entry in os.listdir(zonedir):
+                entrypath = os.path.join(zonedir, entry)
+                tf.add(entrypath, entry)
+    finally:
+        shutil.rmtree(tmpdir)
+
+
+def _run_zic(zonedir, filepaths):
+    """Calls the ``zic`` compiler in a compatible way to get a "fat" binary.
+
+    Recent versions of ``zic`` default to ``-b slim``, while older versions
+    don't even have the ``-b`` option (but default to "fat" binaries). The
+    current version of dateutil does not support Version 2+ TZif files, which
+    causes problems when used in conjunction with "slim" binaries, so this
+    function is used to ensure that we always get a "fat" binary.
+    """
+
+    try:
+        help_text = check_output(["zic", "--help"])
+    except OSError as e:
+        _print_on_nosuchfile(e)
+        raise
+
+    if b"-b " in help_text:
+        bloat_args = ["-b", "fat"]
+    else:
+        bloat_args = []
+
+    check_call(["zic"] + bloat_args + ["-d", zonedir] + filepaths)
+
+
+def _print_on_nosuchfile(e):
+    """Print helpful troubleshooting message
+
+    e is an exception raised by subprocess.check_call()
+
+    """
+    if e.errno == 2:
+        logging.error(
+            "Could not find zic. Perhaps you need to install "
+            "libc-bin or some other package that provides it, "
+            "or it's not in your PATH?")

venv/lib/python3.10/site-packages/mpmath/__init__.py

@@ -0,0 +1,468 @@
+__version__ = '1.3.0'
+
+from .usertools import monitor, timing
+
+from .ctx_fp import FPContext
+from .ctx_mp import MPContext
+from .ctx_iv import MPIntervalContext
+
+fp = FPContext()
+mp = MPContext()
+iv = MPIntervalContext()
+
+fp._mp = mp
+mp._mp = mp
+iv._mp = mp
+mp._fp = fp
+fp._fp = fp
+mp._iv = iv
+fp._iv = iv
+iv._iv = iv
+
+# XXX: extremely bad pickle hack
+from . import ctx_mp as _ctx_mp
+_ctx_mp._mpf_module.mpf = mp.mpf
+_ctx_mp._mpf_module.mpc = mp.mpc
+
+make_mpf = mp.make_mpf
+make_mpc = mp.make_mpc
+
+extraprec = mp.extraprec
+extradps = mp.extradps
+workprec = mp.workprec
+workdps = mp.workdps
+autoprec = mp.autoprec
+maxcalls = mp.maxcalls
+memoize = mp.memoize
+
+mag = mp.mag
+
+bernfrac = mp.bernfrac
+
+qfrom = mp.qfrom
+mfrom = mp.mfrom
+kfrom = mp.kfrom
+taufrom = mp.taufrom
+qbarfrom = mp.qbarfrom
+ellipfun = mp.ellipfun
+jtheta = mp.jtheta
+kleinj = mp.kleinj
+eta = mp.eta
+
+qp = mp.qp
+qhyper = mp.qhyper
+qgamma = mp.qgamma
+qfac = mp.qfac
+
+nint_distance = mp.nint_distance
+
+plot = mp.plot
+cplot = mp.cplot
+splot = mp.splot
+
+odefun = mp.odefun
+
+jacobian = mp.jacobian
+findroot = mp.findroot
+multiplicity = mp.multiplicity
+
+isinf = mp.isinf
+isnan = mp.isnan
+isnormal = mp.isnormal
+isint = mp.isint
+isfinite = mp.isfinite
+almosteq = mp.almosteq
+nan = mp.nan
+rand = mp.rand
+
+absmin = mp.absmin
+absmax = mp.absmax
+
+fraction = mp.fraction
+
+linspace = mp.linspace
+arange = mp.arange
+
+mpmathify = convert = mp.convert
+mpc = mp.mpc
+
+mpi = iv._mpi
+
+nstr = mp.nstr
+nprint = mp.nprint
+chop = mp.chop
+
+fneg = mp.fneg
+fadd = mp.fadd
+fsub = mp.fsub
+fmul = mp.fmul
+fdiv = mp.fdiv
+fprod = mp.fprod
+
+quad = mp.quad
+quadgl = mp.quadgl
+quadts = mp.quadts
+quadosc = mp.quadosc
+quadsubdiv = mp.quadsubdiv
+
+invertlaplace = mp.invertlaplace
+invlaptalbot = mp.invlaptalbot
+invlapstehfest = mp.invlapstehfest
+invlapdehoog = mp.invlapdehoog
+
+pslq = mp.pslq
+identify = mp.identify
+findpoly = mp.findpoly
+
+richardson = mp.richardson
+shanks = mp.shanks
+levin = mp.levin
+cohen_alt = mp.cohen_alt
+nsum = mp.nsum
+nprod = mp.nprod
+difference = mp.difference
+diff = mp.diff
+diffs = mp.diffs
+diffs_prod = mp.diffs_prod
+diffs_exp = mp.diffs_exp
+diffun = mp.diffun
+differint = mp.differint
+taylor = mp.taylor
+pade = mp.pade
+polyval = mp.polyval
+polyroots = mp.polyroots
+fourier = mp.fourier
+fourierval = mp.fourierval
+sumem = mp.sumem
+sumap = mp.sumap
+chebyfit = mp.chebyfit
+limit = mp.limit
+
+matrix = mp.matrix
+eye = mp.eye
+diag = mp.diag
+zeros = mp.zeros
+ones = mp.ones
+hilbert = mp.hilbert
+randmatrix = mp.randmatrix
+swap_row = mp.swap_row
+extend = mp.extend
+norm = mp.norm
+mnorm = mp.mnorm
+
+lu_solve = mp.lu_solve
+lu = mp.lu
+qr = mp.qr
+unitvector = mp.unitvector
+inverse = mp.inverse
+residual = mp.residual
+qr_solve = mp.qr_solve
+cholesky = mp.cholesky
+cholesky_solve = mp.cholesky_solve
+det = mp.det
+cond = mp.cond
+hessenberg = mp.hessenberg
+schur = mp.schur
+eig = mp.eig
+eig_sort = mp.eig_sort
+eigsy = mp.eigsy
+eighe = mp.eighe
+eigh = mp.eigh
+svd_r = mp.svd_r
+svd_c = mp.svd_c
+svd = mp.svd
+gauss_quadrature = mp.gauss_quadrature
+
+expm = mp.expm
+sqrtm = mp.sqrtm
+powm = mp.powm
+logm = mp.logm
+sinm = mp.sinm
+cosm = mp.cosm
+
+mpf = mp.mpf
+j = mp.j
+exp = mp.exp
+expj = mp.expj
+expjpi = mp.expjpi
+ln = mp.ln
+im = mp.im
+re = mp.re
+inf = mp.inf
+ninf = mp.ninf
+sign = mp.sign
+
+eps = mp.eps
+pi = mp.pi
+ln2 = mp.ln2
+ln10 = mp.ln10
+phi = mp.phi
+e = mp.e
+euler = mp.euler
+catalan = mp.catalan
+khinchin = mp.khinchin
+glaisher = mp.glaisher
+apery = mp.apery
+degree = mp.degree
+twinprime = mp.twinprime
+mertens = mp.mertens
+
+ldexp = mp.ldexp
+frexp = mp.frexp
+
+fsum = mp.fsum
+fdot = mp.fdot
+
+sqrt = mp.sqrt
+cbrt = mp.cbrt
+exp = mp.exp
+ln = mp.ln
+log = mp.log
+log10 = mp.log10
+power = mp.power
+cos = mp.cos
+sin = mp.sin
+tan = mp.tan
+cosh = mp.cosh
+sinh = mp.sinh
+tanh = mp.tanh
+acos = mp.acos
+asin = mp.asin
+atan = mp.atan
+asinh = mp.asinh
+acosh = mp.acosh
+atanh = mp.atanh
+sec = mp.sec
+csc = mp.csc
+cot = mp.cot
+sech = mp.sech
+csch = mp.csch
+coth = mp.coth
+asec = mp.asec
+acsc = mp.acsc
+acot = mp.acot
+asech = mp.asech
+acsch = mp.acsch
+acoth = mp.acoth
+cospi = mp.cospi
+sinpi = mp.sinpi
+sinc = mp.sinc
+sincpi = mp.sincpi
+cos_sin = mp.cos_sin
+cospi_sinpi = mp.cospi_sinpi
+fabs = mp.fabs
+re = mp.re
+im = mp.im
+conj = mp.conj
+floor = mp.floor
+ceil = mp.ceil
+nint = mp.nint
+frac = mp.frac
+root = mp.root
+nthroot = mp.nthroot
+hypot = mp.hypot
+fmod = mp.fmod
+ldexp = mp.ldexp
+frexp = mp.frexp
+sign = mp.sign
+arg = mp.arg
+phase = mp.phase
+polar = mp.polar
+rect = mp.rect
+degrees = mp.degrees
+radians = mp.radians
+atan2 = mp.atan2
+fib = mp.fib
+fibonacci = mp.fibonacci
+lambertw = mp.lambertw
+zeta = mp.zeta
+altzeta = mp.altzeta
+gamma = mp.gamma
+rgamma = mp.rgamma
+factorial = mp.factorial
+fac = mp.fac
+fac2 = mp.fac2
+beta = mp.beta
+betainc = mp.betainc
+psi = mp.psi
+#psi0 = mp.psi0
+#psi1 = mp.psi1
+#psi2 = mp.psi2
+#psi3 = mp.psi3
+polygamma = mp.polygamma
+digamma = mp.digamma
+#trigamma = mp.trigamma
+#tetragamma = mp.tetragamma
+#pentagamma = mp.pentagamma
+harmonic = mp.harmonic
+bernoulli = mp.bernoulli
+bernfrac = mp.bernfrac
+stieltjes = mp.stieltjes
+hurwitz = mp.hurwitz
+dirichlet = mp.dirichlet
+bernpoly = mp.bernpoly
+eulerpoly = mp.eulerpoly
+eulernum = mp.eulernum
+polylog = mp.polylog
+clsin = mp.clsin
+clcos = mp.clcos
+gammainc = mp.gammainc
+gammaprod = mp.gammaprod
+binomial = mp.binomial
+rf = mp.rf
+ff = mp.ff
+hyper = mp.hyper
+hyp0f1 = mp.hyp0f1
+hyp1f1 = mp.hyp1f1
+hyp1f2 = mp.hyp1f2
+hyp2f1 = mp.hyp2f1
+hyp2f2 = mp.hyp2f2
+hyp2f0 = mp.hyp2f0
+hyp2f3 = mp.hyp2f3
+hyp3f2 = mp.hyp3f2
+hyperu = mp.hyperu
+hypercomb = mp.hypercomb
+meijerg = mp.meijerg
+appellf1 = mp.appellf1
+appellf2 = mp.appellf2
+appellf3 = mp.appellf3
+appellf4 = mp.appellf4
+hyper2d = mp.hyper2d
+bihyper = mp.bihyper
+erf = mp.erf
+erfc = mp.erfc
+erfi = mp.erfi
+erfinv = mp.erfinv
+npdf = mp.npdf
+ncdf = mp.ncdf
+expint = mp.expint
+e1 = mp.e1
+ei = mp.ei
+li = mp.li
+ci = mp.ci
+si = mp.si
+chi = mp.chi
+shi = mp.shi
+fresnels = mp.fresnels
+fresnelc = mp.fresnelc
+airyai = mp.airyai
+airybi = mp.airybi
+airyaizero = mp.airyaizero
+airybizero = mp.airybizero
+scorergi = mp.scorergi
+scorerhi = mp.scorerhi
+ellipk = mp.ellipk
+ellipe = mp.ellipe
+ellipf = mp.ellipf
+ellippi = mp.ellippi
+elliprc = mp.elliprc
+elliprj = mp.elliprj
+elliprf = mp.elliprf
+elliprd = mp.elliprd
+elliprg = mp.elliprg
+agm = mp.agm
+jacobi = mp.jacobi
+chebyt = mp.chebyt
+chebyu = mp.chebyu
+legendre = mp.legendre
+legenp = mp.legenp
+legenq = mp.legenq
+hermite = mp.hermite
+pcfd = mp.pcfd
+pcfu = mp.pcfu
+pcfv = mp.pcfv
+pcfw = mp.pcfw
+gegenbauer = mp.gegenbauer
+laguerre = mp.laguerre
+spherharm = mp.spherharm
+besselj = mp.besselj
+j0 = mp.j0
+j1 = mp.j1
+besseli = mp.besseli
+bessely = mp.bessely
+besselk = mp.besselk
+besseljzero = mp.besseljzero
+besselyzero = mp.besselyzero
+hankel1 = mp.hankel1
+hankel2 = mp.hankel2
+struveh = mp.struveh
+struvel = mp.struvel
+angerj = mp.angerj
+webere = mp.webere
+lommels1 = mp.lommels1
+lommels2 = mp.lommels2
+whitm = mp.whitm
+whitw = mp.whitw
+ber = mp.ber
+bei = mp.bei
+ker = mp.ker
+kei = mp.kei
+coulombc = mp.coulombc
+coulombf = mp.coulombf
+coulombg = mp.coulombg
+barnesg = mp.barnesg
+superfac = mp.superfac
+hyperfac = mp.hyperfac
+loggamma = mp.loggamma
+siegeltheta = mp.siegeltheta
+siegelz = mp.siegelz
+grampoint = mp.grampoint
+zetazero = mp.zetazero
+riemannr = mp.riemannr
+primepi = mp.primepi
+primepi2 = mp.primepi2
+primezeta = mp.primezeta
+bell = mp.bell
+polyexp = mp.polyexp
+expm1 = mp.expm1
+log1p = mp.log1p
+powm1 = mp.powm1
+unitroots = mp.unitroots
+cyclotomic = mp.cyclotomic
+mangoldt = mp.mangoldt
+secondzeta = mp.secondzeta
+nzeros = mp.nzeros
+backlunds = mp.backlunds
+lerchphi = mp.lerchphi
+stirling1 = mp.stirling1
+stirling2 = mp.stirling2
+squarew = mp.squarew
+trianglew = mp.trianglew
+sawtoothw = mp.sawtoothw
+unit_triangle = mp.unit_triangle
+sigmoid = mp.sigmoid
+
+# be careful when changing this name, don't use test*!
+def runtests():
+    """
+    Run all mpmath tests and print output.
+    """
+    import os.path
+    from inspect import getsourcefile
+    from .tests import runtests as tests
+    testdir = os.path.dirname(os.path.abspath(getsourcefile(tests)))
+    importdir = os.path.abspath(testdir + '/../..')
+    tests.testit(importdir, testdir)
+
+def doctests(filter=[]):
+    import sys
+    from timeit import default_timer as clock
+    for i, arg in enumerate(sys.argv):
+        if '__init__.py' in arg:
+            filter = [sn for sn in sys.argv[i+1:] if not sn.startswith("-")]
+            break
+    import doctest
+    globs = globals().copy()
+    for obj in globs: #sorted(globs.keys()):
+        if filter:
+            if not sum([pat in obj for pat in filter]):
+                continue
+        sys.stdout.write(str(obj) + " ")
+        sys.stdout.flush()
+        t1 = clock()
+        doctest.run_docstring_examples(globs[obj], {}, verbose=("-v" in sys.argv))
+        t2 = clock()
+        print(round(t2-t1, 3))
+
+if __name__ == '__main__':
+    doctests()

venv/lib/python3.10/site-packages/mpmath/ctx_base.py

@@ -0,0 +1,494 @@
+from operator import gt, lt
+
+from .libmp.backend import xrange
+
+from .functions.functions import SpecialFunctions
+from .functions.rszeta import RSCache
+from .calculus.quadrature import QuadratureMethods
+from .calculus.inverselaplace import LaplaceTransformInversionMethods
+from .calculus.calculus import CalculusMethods
+from .calculus.optimization import OptimizationMethods
+from .calculus.odes import ODEMethods
+from .matrices.matrices import MatrixMethods
+from .matrices.calculus import MatrixCalculusMethods
+from .matrices.linalg import LinearAlgebraMethods
+from .matrices.eigen import Eigen
+from .identification import IdentificationMethods
+from .visualization import VisualizationMethods
+
+from . import libmp
+
+class Context(object):
+    pass
+
+class StandardBaseContext(Context,
+    SpecialFunctions,
+    RSCache,
+    QuadratureMethods,
+    LaplaceTransformInversionMethods,
+    CalculusMethods,
+    MatrixMethods,
+    MatrixCalculusMethods,
+    LinearAlgebraMethods,
+    Eigen,
+    IdentificationMethods,
+    OptimizationMethods,
+    ODEMethods,
+    VisualizationMethods):
+
+    NoConvergence = libmp.NoConvergence
+    ComplexResult = libmp.ComplexResult
+
+    def __init__(ctx):
+        ctx._aliases = {}
+        # Call those that need preinitialization (e.g. for wrappers)
+        SpecialFunctions.__init__(ctx)
+        RSCache.__init__(ctx)
+        QuadratureMethods.__init__(ctx)
+        LaplaceTransformInversionMethods.__init__(ctx)
+        CalculusMethods.__init__(ctx)
+        MatrixMethods.__init__(ctx)
+
+    def _init_aliases(ctx):
+        for alias, value in ctx._aliases.items():
+            try:
+                setattr(ctx, alias, getattr(ctx, value))
+            except AttributeError:
+                pass
+
+    _fixed_precision = False
+
+    # XXX
+    verbose = False
+
+    def warn(ctx, msg):
+        print("Warning:", msg)
+
+    def bad_domain(ctx, msg):
+        raise ValueError(msg)
+
+    def _re(ctx, x):
+        if hasattr(x, "real"):
+            return x.real
+        return x
+
+    def _im(ctx, x):
+        if hasattr(x, "imag"):
+            return x.imag
+        return ctx.zero
+
+    def _as_points(ctx, x):
+        return x
+
+    def fneg(ctx, x, **kwargs):
+        return -ctx.convert(x)
+
+    def fadd(ctx, x, y, **kwargs):
+        return ctx.convert(x)+ctx.convert(y)
+
+    def fsub(ctx, x, y, **kwargs):
+        return ctx.convert(x)-ctx.convert(y)
+
+    def fmul(ctx, x, y, **kwargs):
+        return ctx.convert(x)*ctx.convert(y)
+
+    def fdiv(ctx, x, y, **kwargs):
+        return ctx.convert(x)/ctx.convert(y)
+
+    def fsum(ctx, args, absolute=False, squared=False):
+        if absolute:
+            if squared:
+                return sum((abs(x)**2 for x in args), ctx.zero)
+            return sum((abs(x) for x in args), ctx.zero)
+        if squared:
+            return sum((x**2 for x in args), ctx.zero)
+        return sum(args, ctx.zero)
+
+    def fdot(ctx, xs, ys=None, conjugate=False):
+        if ys is not None:
+            xs = zip(xs, ys)
+        if conjugate:
+            cf = ctx.conj
+            return sum((x*cf(y) for (x,y) in xs), ctx.zero)
+        else:
+            return sum((x*y for (x,y) in xs), ctx.zero)
+
+    def fprod(ctx, args):
+        prod = ctx.one
+        for arg in args:
+            prod *= arg
+        return prod
+
+    def nprint(ctx, x, n=6, **kwargs):
+        """
+        Equivalent to ``print(nstr(x, n))``.
+        """
+        print(ctx.nstr(x, n, **kwargs))
+
+    def chop(ctx, x, tol=None):
+        """
+        Chops off small real or imaginary parts, or converts
+        numbers close to zero to exact zeros. The input can be a
+        single number or an iterable::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> chop(5+1e-10j, tol=1e-9)
+            mpf('5.0')
+            >>> nprint(chop([1.0, 1e-20, 3+1e-18j, -4, 2]))
+            [1.0, 0.0, 3.0, -4.0, 2.0]
+
+        The tolerance defaults to ``100*eps``.
+        """
+        if tol is None:
+            tol = 100*ctx.eps
+        try:
+            x = ctx.convert(x)
+            absx = abs(x)
+            if abs(x) < tol:
+                return ctx.zero
+            if ctx._is_complex_type(x):
+                #part_tol = min(tol, absx*tol)
+                part_tol = max(tol, absx*tol)
+                if abs(x.imag) < part_tol:
+                    return x.real
+                if abs(x.real) < part_tol:
+                    return ctx.mpc(0, x.imag)
+        except TypeError:
+            if isinstance(x, ctx.matrix):
+                return x.apply(lambda a: ctx.chop(a, tol))
+            if hasattr(x, "__iter__"):
+                return [ctx.chop(a, tol) for a in x]
+        return x
+
+    def almosteq(ctx, s, t, rel_eps=None, abs_eps=None):
+        r"""
+        Determine whether the difference between `s` and `t` is smaller
+        than a given epsilon, either relatively or absolutely.
+
+        Both a maximum relative difference and a maximum difference
+        ('epsilons') may be specified. The absolute difference is
+        defined as `|s-t|` and the relative difference is defined
+        as `|s-t|/\max(|s|, |t|)`.
+
+        If only one epsilon is given, both are set to the same value.
+        If none is given, both epsilons are set to `2^{-p+m}` where
+        `p` is the current working precision and `m` is a small
+        integer. The default setting typically allows :func:`~mpmath.almosteq`
+        to be used to check for mathematical equality
+        in the presence of small rounding errors.
+
+        **Examples**
+
+            >>> from mpmath import *
+            >>> mp.dps = 15
+            >>> almosteq(3.141592653589793, 3.141592653589790)
+            True
+            >>> almosteq(3.141592653589793, 3.141592653589700)
+            False
+            >>> almosteq(3.141592653589793, 3.141592653589700, 1e-10)
+            True
+            >>> almosteq(1e-20, 2e-20)
+            True
+            >>> almosteq(1e-20, 2e-20, rel_eps=0, abs_eps=0)
+            False
+
+        """
+        t = ctx.convert(t)
+        if abs_eps is None and rel_eps is None:
+            rel_eps = abs_eps = ctx.ldexp(1, -ctx.prec+4)
+        if abs_eps is None:
+            abs_eps = rel_eps
+        elif rel_eps is None:
+            rel_eps = abs_eps
+        diff = abs(s-t)
+        if diff <= abs_eps:
+            return True
+        abss = abs(s)
+        abst = abs(t)
+        if abss < abst:
+            err = diff/abst
+        else:
+            err = diff/abss
+        return err <= rel_eps
+
+    def arange(ctx, *args):
+        r"""
+        This is a generalized version of Python's :func:`~mpmath.range` function
+        that accepts fractional endpoints and step sizes and
+        returns a list of ``mpf`` instances. Like :func:`~mpmath.range`,
+        :func:`~mpmath.arange` can be called with 1, 2 or 3 arguments:
+
+        ``arange(b)``
+            `[0, 1, 2, \ldots, x]`
+        ``arange(a, b)``
+            `[a, a+1, a+2, \ldots, x]`
+        ``arange(a, b, h)``
+            `[a, a+h, a+h, \ldots, x]`
+
+        where `b-1 \le x < b` (in the third case, `b-h \le x < b`).
+
+        Like Python's :func:`~mpmath.range`, the endpoint is not included. To
+        produce ranges where the endpoint is included, :func:`~mpmath.linspace`
+        is more convenient.
+
+        **Examples**
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> arange(4)
+            [mpf('0.0'), mpf('1.0'), mpf('2.0'), mpf('3.0')]
+            >>> arange(1, 2, 0.25)
+            [mpf('1.0'), mpf('1.25'), mpf('1.5'), mpf('1.75')]
+            >>> arange(1, -1, -0.75)
+            [mpf('1.0'), mpf('0.25'), mpf('-0.5')]
+
+        """
+        if not len(args) <= 3:
+            raise TypeError('arange expected at most 3 arguments, got %i'
+                            % len(args))
+        if not len(args) >= 1:
+            raise TypeError('arange expected at least 1 argument, got %i'
+                            % len(args))
+        # set default
+        a = 0
+        dt = 1
+        # interpret arguments
+        if len(args) == 1:
+            b = args[0]
+        elif len(args) >= 2:
+            a = args[0]
+            b = args[1]
+        if len(args) == 3:
+            dt = args[2]
+        a, b, dt = ctx.mpf(a), ctx.mpf(b), ctx.mpf(dt)
+        assert a + dt != a, 'dt is too small and would cause an infinite loop'
+        # adapt code for sign of dt
+        if a > b:
+            if dt > 0:
+                return []
+            op = gt
+        else:
+            if dt < 0:
+                return []
+            op = lt
+        # create list
+        result = []
+        i = 0
+        t = a
+        while 1:
+            t = a + dt*i
+            i += 1
+            if op(t, b):
+                result.append(t)
+            else:
+                break
+        return result
+
+    def linspace(ctx, *args, **kwargs):
+        """
+        ``linspace(a, b, n)`` returns a list of `n` evenly spaced
+        samples from `a` to `b`. The syntax ``linspace(mpi(a,b), n)``
+        is also valid.
+
+        This function is often more convenient than :func:`~mpmath.arange`
+        for partitioning an interval into subintervals, since
+        the endpoint is included::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> linspace(1, 4, 4)
+            [mpf('1.0'), mpf('2.0'), mpf('3.0'), mpf('4.0')]
+
+        You may also provide the keyword argument ``endpoint=False``::
+
+            >>> linspace(1, 4, 4, endpoint=False)
+            [mpf('1.0'), mpf('1.75'), mpf('2.5'), mpf('3.25')]
+
+        """
+        if len(args) == 3:
+            a = ctx.mpf(args[0])
+            b = ctx.mpf(args[1])
+            n = int(args[2])
+        elif len(args) == 2:
+            assert hasattr(args[0], '_mpi_')
+            a = args[0].a
+            b = args[0].b
+            n = int(args[1])
+        else:
+            raise TypeError('linspace expected 2 or 3 arguments, got %i' \
+                            % len(args))
+        if n < 1:
+            raise ValueError('n must be greater than 0')
+        if not 'endpoint' in kwargs or kwargs['endpoint']:
+            if n == 1:
+                return [ctx.mpf(a)]
+            step = (b - a) / ctx.mpf(n - 1)
+            y = [i*step + a for i in xrange(n)]
+            y[-1] = b
+        else:
+            step = (b - a) / ctx.mpf(n)
+            y = [i*step + a for i in xrange(n)]
+        return y
+
+    def cos_sin(ctx, z, **kwargs):
+        return ctx.cos(z, **kwargs), ctx.sin(z, **kwargs)
+
+    def cospi_sinpi(ctx, z, **kwargs):
+        return ctx.cospi(z, **kwargs), ctx.sinpi(z, **kwargs)
+
+    def _default_hyper_maxprec(ctx, p):
+        return int(1000 * p**0.25 + 4*p)
+
+    _gcd = staticmethod(libmp.gcd)
+    list_primes = staticmethod(libmp.list_primes)
+    isprime = staticmethod(libmp.isprime)
+    bernfrac = staticmethod(libmp.bernfrac)
+    moebius = staticmethod(libmp.moebius)
+    _ifac = staticmethod(libmp.ifac)
+    _eulernum = staticmethod(libmp.eulernum)
+    _stirling1 = staticmethod(libmp.stirling1)
+    _stirling2 = staticmethod(libmp.stirling2)
+
+    def sum_accurately(ctx, terms, check_step=1):
+        prec = ctx.prec
+        try:
+            extraprec = 10
+            while 1:
+                ctx.prec = prec + extraprec + 5
+                max_mag = ctx.ninf
+                s = ctx.zero
+                k = 0
+                for term in terms():
+                    s += term
+                    if (not k % check_step) and term:
+                        term_mag = ctx.mag(term)
+                        max_mag = max(max_mag, term_mag)
+                        sum_mag = ctx.mag(s)
+                        if sum_mag - term_mag > ctx.prec:
+                            break
+                    k += 1
+                cancellation = max_mag - sum_mag
+                if cancellation != cancellation:
+                    break
+                if cancellation < extraprec or ctx._fixed_precision:
+                    break
+                extraprec += min(ctx.prec, cancellation)
+            return s
+        finally:
+            ctx.prec = prec
+
+    def mul_accurately(ctx, factors, check_step=1):
+        prec = ctx.prec
+        try:
+            extraprec = 10
+            while 1:
+                ctx.prec = prec + extraprec + 5
+                max_mag = ctx.ninf
+                one = ctx.one
+                s = one
+                k = 0
+                for factor in factors():
+                    s *= factor
+                    term = factor - one
+                    if (not k % check_step):
+                        term_mag = ctx.mag(term)
+                        max_mag = max(max_mag, term_mag)
+                        sum_mag = ctx.mag(s-one)
+                        #if sum_mag - term_mag > ctx.prec:
+                        #    break
+                        if -term_mag > ctx.prec:
+                            break
+                    k += 1
+                cancellation = max_mag - sum_mag
+                if cancellation != cancellation:
+                    break
+                if cancellation < extraprec or ctx._fixed_precision:
+                    break
+                extraprec += min(ctx.prec, cancellation)
+            return s
+        finally:
+            ctx.prec = prec
+
+    def power(ctx, x, y):
+        r"""Converts `x` and `y` to mpmath numbers and evaluates
+        `x^y = \exp(y \log(x))`::
+
+            >>> from mpmath import *
+            >>> mp.dps = 30; mp.pretty = True
+            >>> power(2, 0.5)
+            1.41421356237309504880168872421
+
+        This shows the leading few digits of a large Mersenne prime
+        (performing the exact calculation ``2**43112609-1`` and
+        displaying the result in Python would be very slow)::
+
+            >>> power(2, 43112609)-1
+            3.16470269330255923143453723949e+12978188
+        """
+        return ctx.convert(x) ** ctx.convert(y)
+
+    def _zeta_int(ctx, n):
+        return ctx.zeta(n)
+
+    def maxcalls(ctx, f, N):
+        """
+        Return a wrapped copy of *f* that raises ``NoConvergence`` when *f*
+        has been called more than *N* times::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15
+            >>> f = maxcalls(sin, 10)
+            >>> print(sum(f(n) for n in range(10)))
+            1.95520948210738
+            >>> f(10) # doctest: +IGNORE_EXCEPTION_DETAIL
+            Traceback (most recent call last):
+              ...
+            NoConvergence: maxcalls: function evaluated 10 times
+
+        """
+        counter = [0]
+        def f_maxcalls_wrapped(*args, **kwargs):
+            counter[0] += 1
+            if counter[0] > N:
+                raise ctx.NoConvergence("maxcalls: function evaluated %i times" % N)
+            return f(*args, **kwargs)
+        return f_maxcalls_wrapped
+
+    def memoize(ctx, f):
+        """
+        Return a wrapped copy of *f* that caches computed values, i.e.
+        a memoized copy of *f*. Values are only reused if the cached precision
+        is equal to or higher than the working precision::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = True
+            >>> f = memoize(maxcalls(sin, 1))
+            >>> f(2)
+            0.909297426825682
+            >>> f(2)
+            0.909297426825682
+            >>> mp.dps = 25
+            >>> f(2) # doctest: +IGNORE_EXCEPTION_DETAIL
+            Traceback (most recent call last):
+              ...
+            NoConvergence: maxcalls: function evaluated 1 times
+
+        """
+        f_cache = {}
+        def f_cached(*args, **kwargs):
+            if kwargs:
+                key = args, tuple(kwargs.items())
+            else:
+                key = args
+            prec = ctx.prec
+            if key in f_cache:
+                cprec, cvalue = f_cache[key]
+                if cprec >= prec:
+                    return +cvalue
+            value = f(*args, **kwargs)
+            f_cache[key] = (prec, value)
+            return value
+        f_cached.__name__ = f.__name__
+        f_cached.__doc__ = f.__doc__
+        return f_cached

venv/lib/python3.10/site-packages/mpmath/ctx_fp.py

@@ -0,0 +1,253 @@
+from .ctx_base import StandardBaseContext
+
+import math
+import cmath
+from . import math2
+
+from . import function_docs
+
+from .libmp import mpf_bernoulli, to_float, int_types
+from . import libmp
+
+class FPContext(StandardBaseContext):
+    """
+    Context for fast low-precision arithmetic (53-bit precision, giving at most
+    about 15-digit accuracy), using Python's builtin float and complex.
+    """
+
+    def __init__(ctx):
+        StandardBaseContext.__init__(ctx)
+
+        # Override SpecialFunctions implementation
+        ctx.loggamma = math2.loggamma
+        ctx._bernoulli_cache = {}
+        ctx.pretty = False
+
+        ctx._init_aliases()
+
+    _mpq = lambda cls, x: float(x[0])/x[1]
+
+    NoConvergence = libmp.NoConvergence
+
+    def _get_prec(ctx): return 53
+    def _set_prec(ctx, p): return
+    def _get_dps(ctx): return 15
+    def _set_dps(ctx, p): return
+
+    _fixed_precision = True
+
+    prec = property(_get_prec, _set_prec)
+    dps = property(_get_dps, _set_dps)
+
+    zero = 0.0
+    one = 1.0
+    eps = math2.EPS
+    inf = math2.INF
+    ninf = math2.NINF
+    nan = math2.NAN
+    j = 1j
+
+    # Called by SpecialFunctions.__init__()
+    @classmethod
+    def _wrap_specfun(cls, name, f, wrap):
+        if wrap:
+            def f_wrapped(ctx, *args, **kwargs):
+                convert = ctx.convert
+                args = [convert(a) for a in args]
+                return f(ctx, *args, **kwargs)
+        else:
+            f_wrapped = f
+        f_wrapped.__doc__ = function_docs.__dict__.get(name, f.__doc__)
+        setattr(cls, name, f_wrapped)
+
+    def bernoulli(ctx, n):
+        cache = ctx._bernoulli_cache
+        if n in cache:
+            return cache[n]
+        cache[n] = to_float(mpf_bernoulli(n, 53, 'n'), strict=True)
+        return cache[n]
+
+    pi = math2.pi
+    e = math2.e
+    euler = math2.euler
+    sqrt2 = 1.4142135623730950488
+    sqrt5 = 2.2360679774997896964
+    phi = 1.6180339887498948482
+    ln2 = 0.69314718055994530942
+    ln10 = 2.302585092994045684
+    euler = 0.57721566490153286061
+    catalan = 0.91596559417721901505
+    khinchin = 2.6854520010653064453
+    apery = 1.2020569031595942854
+    glaisher = 1.2824271291006226369
+
+    absmin = absmax = abs
+
+    def is_special(ctx, x):
+        return x - x != 0.0
+
+    def isnan(ctx, x):
+        return x != x
+
+    def isinf(ctx, x):
+        return abs(x) == math2.INF
+
+    def isnormal(ctx, x):
+        if x:
+            return x - x == 0.0
+        return False
+
+    def isnpint(ctx, x):
+        if type(x) is complex:
+            if x.imag:
+                return False
+            x = x.real
+        return x <= 0.0 and round(x) == x
+
+    mpf = float
+    mpc = complex
+
+    def convert(ctx, x):
+        try:
+            return float(x)
+        except:
+            return complex(x)
+
+    power = staticmethod(math2.pow)
+    sqrt = staticmethod(math2.sqrt)
+    exp = staticmethod(math2.exp)
+    ln = log = staticmethod(math2.log)
+    cos = staticmethod(math2.cos)
+    sin = staticmethod(math2.sin)
+    tan = staticmethod(math2.tan)
+    cos_sin = staticmethod(math2.cos_sin)
+    acos = staticmethod(math2.acos)
+    asin = staticmethod(math2.asin)
+    atan = staticmethod(math2.atan)
+    cosh = staticmethod(math2.cosh)
+    sinh = staticmethod(math2.sinh)
+    tanh = staticmethod(math2.tanh)
+    gamma = staticmethod(math2.gamma)
+    rgamma = staticmethod(math2.rgamma)
+    fac = factorial = staticmethod(math2.factorial)
+    floor = staticmethod(math2.floor)
+    ceil = staticmethod(math2.ceil)
+    cospi = staticmethod(math2.cospi)
+    sinpi = staticmethod(math2.sinpi)
+    cbrt = staticmethod(math2.cbrt)
+    _nthroot = staticmethod(math2.nthroot)
+    _ei = staticmethod(math2.ei)
+    _e1 = staticmethod(math2.e1)
+    _zeta = _zeta_int = staticmethod(math2.zeta)
+
+    # XXX: math2
+    def arg(ctx, z):
+        z = complex(z)
+        return math.atan2(z.imag, z.real)
+
+    def expj(ctx, x):
+        return ctx.exp(ctx.j*x)
+
+    def expjpi(ctx, x):
+        return ctx.exp(ctx.j*ctx.pi*x)
+
+    ldexp = math.ldexp
+    frexp = math.frexp
+
+    def mag(ctx, z):
+        if z:
+            return ctx.frexp(abs(z))[1]
+        return ctx.ninf
+
+    def isint(ctx, z):
+        if hasattr(z, "imag"):   # float/int don't have .real/.imag in py2.5
+            if z.imag:
+                return False
+            z = z.real
+        try:
+            return z == int(z)
+        except:
+            return False
+
+    def nint_distance(ctx, z):
+        if hasattr(z, "imag"):   # float/int don't have .real/.imag in py2.5
+            n = round(z.real)
+        else:
+            n = round(z)
+        if n == z:
+            return n, ctx.ninf
+        return n, ctx.mag(abs(z-n))
+
+    def _convert_param(ctx, z):
+        if type(z) is tuple:
+            p, q = z
+            return ctx.mpf(p) / q, 'R'
+        if hasattr(z, "imag"):    # float/int don't have .real/.imag in py2.5
+            intz = int(z.real)
+        else:
+            intz = int(z)
+        if z == intz:
+            return intz, 'Z'
+        return z, 'R'
+
+    def _is_real_type(ctx, z):
+        return isinstance(z, float) or isinstance(z, int_types)
+
+    def _is_complex_type(ctx, z):
+        return isinstance(z, complex)
+
+    def hypsum(ctx, p, q, types, coeffs, z, maxterms=6000, **kwargs):
+        coeffs = list(coeffs)
+        num = range(p)
+        den = range(p,p+q)
+        tol = ctx.eps
+        s = t = 1.0
+        k = 0
+        while 1:
+            for i in num: t *= (coeffs[i]+k)
+            for i in den: t /= (coeffs[i]+k)
+            k += 1; t /= k; t *= z; s += t
+            if abs(t) < tol:
+                return s
+            if k > maxterms:
+                raise ctx.NoConvergence
+
+    def atan2(ctx, x, y):
+        return math.atan2(x, y)
+
+    def psi(ctx, m, z):
+        m = int(m)
+        if m == 0:
+            return ctx.digamma(z)
+        return (-1)**(m+1) * ctx.fac(m) * ctx.zeta(m+1, z)
+
+    digamma = staticmethod(math2.digamma)
+
+    def harmonic(ctx, x):
+        x = ctx.convert(x)
+        if x == 0 or x == 1:
+            return x
+        return ctx.digamma(x+1) + ctx.euler
+
+    nstr = str
+
+    def to_fixed(ctx, x, prec):
+        return int(math.ldexp(x, prec))
+
+    def rand(ctx):
+        import random
+        return random.random()
+
+    _erf = staticmethod(math2.erf)
+    _erfc = staticmethod(math2.erfc)
+
+    def sum_accurately(ctx, terms, check_step=1):
+        s = ctx.zero
+        k = 0
+        for term in terms():
+            s += term
+            if (not k % check_step) and term:
+                if abs(term) <= 1e-18*abs(s):
+                    break
+            k += 1
+        return s

venv/lib/python3.10/site-packages/mpmath/ctx_iv.py

@@ -0,0 +1,551 @@
+import operator
+
+from . import libmp
+
+from .libmp.backend import basestring
+
+from .libmp import (
+    int_types, MPZ_ONE,
+    prec_to_dps, dps_to_prec, repr_dps,
+    round_floor, round_ceiling,
+    fzero, finf, fninf, fnan,
+    mpf_le, mpf_neg,
+    from_int, from_float, from_str, from_rational,
+    mpi_mid, mpi_delta, mpi_str,
+    mpi_abs, mpi_pos, mpi_neg, mpi_add, mpi_sub,
+    mpi_mul, mpi_div, mpi_pow_int, mpi_pow,
+    mpi_from_str,
+    mpci_pos, mpci_neg, mpci_add, mpci_sub, mpci_mul, mpci_div, mpci_pow,
+    mpci_abs, mpci_pow, mpci_exp, mpci_log,
+    ComplexResult,
+    mpf_hash, mpc_hash)
+from .matrices.matrices import _matrix
+
+mpi_zero = (fzero, fzero)
+
+from .ctx_base import StandardBaseContext
+
+new = object.__new__
+
+def convert_mpf_(x, prec, rounding):
+    if hasattr(x, "_mpf_"): return x._mpf_
+    if isinstance(x, int_types): return from_int(x, prec, rounding)
+    if isinstance(x, float): return from_float(x, prec, rounding)
+    if isinstance(x, basestring): return from_str(x, prec, rounding)
+    raise NotImplementedError
+
+
+class ivmpf(object):
+    """
+    Interval arithmetic class. Precision is controlled by iv.prec.
+    """
+
+    def __new__(cls, x=0):
+        return cls.ctx.convert(x)
+
+    def cast(self, cls, f_convert):
+        a, b = self._mpi_
+        if a == b:
+            return cls(f_convert(a))
+        raise ValueError
+
+    def __int__(self):
+        return self.cast(int, libmp.to_int)
+
+    def __float__(self):
+        return self.cast(float, libmp.to_float)
+
+    def __complex__(self):
+        return self.cast(complex, libmp.to_float)
+
+    def __hash__(self):
+        a, b = self._mpi_
+        if a == b:
+            return mpf_hash(a)
+        else:
+            return hash(self._mpi_)
+
+    @property
+    def real(self): return self
+
+    @property
+    def imag(self): return self.ctx.zero
+
+    def conjugate(self): return self
+
+    @property
+    def a(self):
+        a, b = self._mpi_
+        return self.ctx.make_mpf((a, a))
+
+    @property
+    def b(self):
+        a, b = self._mpi_
+        return self.ctx.make_mpf((b, b))
+
+    @property
+    def mid(self):
+        ctx = self.ctx
+        v = mpi_mid(self._mpi_, ctx.prec)
+        return ctx.make_mpf((v, v))
+
+    @property
+    def delta(self):
+        ctx = self.ctx
+        v = mpi_delta(self._mpi_, ctx.prec)
+        return ctx.make_mpf((v,v))
+
+    @property
+    def _mpci_(self):
+        return self._mpi_, mpi_zero
+
+    def _compare(*args):
+        raise TypeError("no ordering relation is defined for intervals")
+
+    __gt__ = _compare
+    __le__ = _compare
+    __gt__ = _compare
+    __ge__ = _compare
+
+    def __contains__(self, t):
+        t = self.ctx.mpf(t)
+        return (self.a <= t.a) and (t.b <= self.b)
+
+    def __str__(self):
+        return mpi_str(self._mpi_, self.ctx.prec)
+
+    def __repr__(self):
+        if self.ctx.pretty:
+            return str(self)
+        a, b = self._mpi_
+        n = repr_dps(self.ctx.prec)
+        a = libmp.to_str(a, n)
+        b = libmp.to_str(b, n)
+        return "mpi(%r, %r)" % (a, b)
+
+    def _compare(s, t, cmpfun):
+        if not hasattr(t, "_mpi_"):
+            try:
+                t = s.ctx.convert(t)
+            except:
+                return NotImplemented
+        return cmpfun(s._mpi_, t._mpi_)
+
+    def __eq__(s, t): return s._compare(t, libmp.mpi_eq)
+    def __ne__(s, t): return s._compare(t, libmp.mpi_ne)
+    def __lt__(s, t): return s._compare(t, libmp.mpi_lt)
+    def __le__(s, t): return s._compare(t, libmp.mpi_le)
+    def __gt__(s, t): return s._compare(t, libmp.mpi_gt)
+    def __ge__(s, t): return s._compare(t, libmp.mpi_ge)
+
+    def __abs__(self):
+        return self.ctx.make_mpf(mpi_abs(self._mpi_, self.ctx.prec))
+    def __pos__(self):
+        return self.ctx.make_mpf(mpi_pos(self._mpi_, self.ctx.prec))
+    def __neg__(self):
+        return self.ctx.make_mpf(mpi_neg(self._mpi_, self.ctx.prec))
+
+    def ae(s, t, rel_eps=None, abs_eps=None):
+        return s.ctx.almosteq(s, t, rel_eps, abs_eps)
+
+class ivmpc(object):
+
+    def __new__(cls, re=0, im=0):
+        re = cls.ctx.convert(re)
+        im = cls.ctx.convert(im)
+        y = new(cls)
+        y._mpci_ = re._mpi_, im._mpi_
+        return y
+
+    def __hash__(self):
+        (a, b), (c,d) = self._mpci_
+        if a == b and c == d:
+            return mpc_hash((a, c))
+        else:
+            return hash(self._mpci_)
+
+    def __repr__(s):
+        if s.ctx.pretty:
+            return str(s)
+        return "iv.mpc(%s, %s)" % (repr(s.real), repr(s.imag))
+
+    def __str__(s):
+        return "(%s + %s*j)" % (str(s.real), str(s.imag))
+
+    @property
+    def a(self):
+        (a, b), (c,d) = self._mpci_
+        return self.ctx.make_mpf((a, a))
+
+    @property
+    def b(self):
+        (a, b), (c,d) = self._mpci_
+        return self.ctx.make_mpf((b, b))
+
+    @property
+    def c(self):
+        (a, b), (c,d) = self._mpci_
+        return self.ctx.make_mpf((c, c))
+
+    @property
+    def d(self):
+        (a, b), (c,d) = self._mpci_
+        return self.ctx.make_mpf((d, d))
+
+    @property
+    def real(s):
+        return s.ctx.make_mpf(s._mpci_[0])
+
+    @property
+    def imag(s):
+        return s.ctx.make_mpf(s._mpci_[1])
+
+    def conjugate(s):
+        a, b = s._mpci_
+        return s.ctx.make_mpc((a, mpf_neg(b)))
+
+    def overlap(s, t):
+        t = s.ctx.convert(t)
+        real_overlap = (s.a <= t.a <= s.b) or (s.a <= t.b <= s.b) or (t.a <= s.a <= t.b) or (t.a <= s.b <= t.b)
+        imag_overlap = (s.c <= t.c <= s.d) or (s.c <= t.d <= s.d) or (t.c <= s.c <= t.d) or (t.c <= s.d <= t.d)
+        return real_overlap and imag_overlap
+
+    def __contains__(s, t):
+        t = s.ctx.convert(t)
+        return t.real in s.real and t.imag in s.imag
+
+    def _compare(s, t, ne=False):
+        if not isinstance(t, s.ctx._types):
+            try:
+                t = s.ctx.convert(t)
+            except:
+                return NotImplemented
+        if hasattr(t, '_mpi_'):
+            tval = t._mpi_, mpi_zero
+        elif hasattr(t, '_mpci_'):
+            tval = t._mpci_
+        if ne:
+            return s._mpci_ != tval
+        return s._mpci_ == tval
+
+    def __eq__(s, t): return s._compare(t)
+    def __ne__(s, t): return s._compare(t, True)
+
+    def __lt__(s, t): raise TypeError("complex intervals cannot be ordered")
+    __le__ = __gt__ = __ge__ = __lt__
+
+    def __neg__(s): return s.ctx.make_mpc(mpci_neg(s._mpci_, s.ctx.prec))
+    def __pos__(s): return s.ctx.make_mpc(mpci_pos(s._mpci_, s.ctx.prec))
+    def __abs__(s): return s.ctx.make_mpf(mpci_abs(s._mpci_, s.ctx.prec))
+
+    def ae(s, t, rel_eps=None, abs_eps=None):
+        return s.ctx.almosteq(s, t, rel_eps, abs_eps)
+
+def _binary_op(f_real, f_complex):
+    def g_complex(ctx, sval, tval):
+        return ctx.make_mpc(f_complex(sval, tval, ctx.prec))
+    def g_real(ctx, sval, tval):
+        try:
+            return ctx.make_mpf(f_real(sval, tval, ctx.prec))
+        except ComplexResult:
+            sval = (sval, mpi_zero)
+            tval = (tval, mpi_zero)
+            return g_complex(ctx, sval, tval)
+    def lop_real(s, t):
+        if isinstance(t, _matrix): return NotImplemented
+        ctx = s.ctx
+        if not isinstance(t, ctx._types): t = ctx.convert(t)
+        if hasattr(t, "_mpi_"): return g_real(ctx, s._mpi_, t._mpi_)
+        if hasattr(t, "_mpci_"): return g_complex(ctx, (s._mpi_, mpi_zero), t._mpci_)
+        return NotImplemented
+    def rop_real(s, t):
+        ctx = s.ctx
+        if not isinstance(t, ctx._types): t = ctx.convert(t)
+        if hasattr(t, "_mpi_"): return g_real(ctx, t._mpi_, s._mpi_)
+        if hasattr(t, "_mpci_"): return g_complex(ctx, t._mpci_, (s._mpi_, mpi_zero))
+        return NotImplemented
+    def lop_complex(s, t):
+        if isinstance(t, _matrix): return NotImplemented
+        ctx = s.ctx
+        if not isinstance(t, s.ctx._types):
+            try:
+                t = s.ctx.convert(t)
+            except (ValueError, TypeError):
+                return NotImplemented
+        return g_complex(ctx, s._mpci_, t._mpci_)
+    def rop_complex(s, t):
+        ctx = s.ctx
+        if not isinstance(t, s.ctx._types):
+            t = s.ctx.convert(t)
+        return g_complex(ctx, t._mpci_, s._mpci_)
+    return lop_real, rop_real, lop_complex, rop_complex
+
+ivmpf.__add__, ivmpf.__radd__, ivmpc.__add__, ivmpc.__radd__ = _binary_op(mpi_add, mpci_add)
+ivmpf.__sub__, ivmpf.__rsub__, ivmpc.__sub__, ivmpc.__rsub__ = _binary_op(mpi_sub, mpci_sub)
+ivmpf.__mul__, ivmpf.__rmul__, ivmpc.__mul__, ivmpc.__rmul__ = _binary_op(mpi_mul, mpci_mul)
+ivmpf.__div__, ivmpf.__rdiv__, ivmpc.__div__, ivmpc.__rdiv__ = _binary_op(mpi_div, mpci_div)
+ivmpf.__pow__, ivmpf.__rpow__, ivmpc.__pow__, ivmpc.__rpow__ = _binary_op(mpi_pow, mpci_pow)
+
+ivmpf.__truediv__ = ivmpf.__div__; ivmpf.__rtruediv__ = ivmpf.__rdiv__
+ivmpc.__truediv__ = ivmpc.__div__; ivmpc.__rtruediv__ = ivmpc.__rdiv__
+
+class ivmpf_constant(ivmpf):
+    def __new__(cls, f):
+        self = new(cls)
+        self._f = f
+        return self
+    def _get_mpi_(self):
+        prec = self.ctx._prec[0]
+        a = self._f(prec, round_floor)
+        b = self._f(prec, round_ceiling)
+        return a, b
+    _mpi_ = property(_get_mpi_)
+
+class MPIntervalContext(StandardBaseContext):
+
+    def __init__(ctx):
+        ctx.mpf = type('ivmpf', (ivmpf,), {})
+        ctx.mpc = type('ivmpc', (ivmpc,), {})
+        ctx._types = (ctx.mpf, ctx.mpc)
+        ctx._constant = type('ivmpf_constant', (ivmpf_constant,), {})
+        ctx._prec = [53]
+        ctx._set_prec(53)
+        ctx._constant._ctxdata = ctx.mpf._ctxdata = ctx.mpc._ctxdata = [ctx.mpf, new, ctx._prec]
+        ctx._constant.ctx = ctx.mpf.ctx = ctx.mpc.ctx = ctx
+        ctx.pretty = False
+        StandardBaseContext.__init__(ctx)
+        ctx._init_builtins()
+
+    def _mpi(ctx, a, b=None):
+        if b is None:
+            return ctx.mpf(a)
+        return ctx.mpf((a,b))
+
+    def _init_builtins(ctx):
+        ctx.one = ctx.mpf(1)
+        ctx.zero = ctx.mpf(0)
+        ctx.inf = ctx.mpf('inf')
+        ctx.ninf = -ctx.inf
+        ctx.nan = ctx.mpf('nan')
+        ctx.j = ctx.mpc(0,1)
+        ctx.exp = ctx._wrap_mpi_function(libmp.mpi_exp, libmp.mpci_exp)
+        ctx.sqrt = ctx._wrap_mpi_function(libmp.mpi_sqrt)
+        ctx.ln = ctx._wrap_mpi_function(libmp.mpi_log, libmp.mpci_log)
+        ctx.cos = ctx._wrap_mpi_function(libmp.mpi_cos, libmp.mpci_cos)
+        ctx.sin = ctx._wrap_mpi_function(libmp.mpi_sin, libmp.mpci_sin)
+        ctx.tan = ctx._wrap_mpi_function(libmp.mpi_tan)
+        ctx.gamma = ctx._wrap_mpi_function(libmp.mpi_gamma, libmp.mpci_gamma)
+        ctx.loggamma = ctx._wrap_mpi_function(libmp.mpi_loggamma, libmp.mpci_loggamma)
+        ctx.rgamma = ctx._wrap_mpi_function(libmp.mpi_rgamma, libmp.mpci_rgamma)
+        ctx.factorial = ctx._wrap_mpi_function(libmp.mpi_factorial, libmp.mpci_factorial)
+        ctx.fac = ctx.factorial
+
+        ctx.eps = ctx._constant(lambda prec, rnd: (0, MPZ_ONE, 1-prec, 1))
+        ctx.pi = ctx._constant(libmp.mpf_pi)
+        ctx.e = ctx._constant(libmp.mpf_e)
+        ctx.ln2 = ctx._constant(libmp.mpf_ln2)
+        ctx.ln10 = ctx._constant(libmp.mpf_ln10)
+        ctx.phi = ctx._constant(libmp.mpf_phi)
+        ctx.euler = ctx._constant(libmp.mpf_euler)
+        ctx.catalan = ctx._constant(libmp.mpf_catalan)
+        ctx.glaisher = ctx._constant(libmp.mpf_glaisher)
+        ctx.khinchin = ctx._constant(libmp.mpf_khinchin)
+        ctx.twinprime = ctx._constant(libmp.mpf_twinprime)
+
+    def _wrap_mpi_function(ctx, f_real, f_complex=None):
+        def g(x, **kwargs):
+            if kwargs:
+                prec = kwargs.get('prec', ctx._prec[0])
+            else:
+                prec = ctx._prec[0]
+            x = ctx.convert(x)
+            if hasattr(x, "_mpi_"):
+                return ctx.make_mpf(f_real(x._mpi_, prec))
+            if hasattr(x, "_mpci_"):
+                return ctx.make_mpc(f_complex(x._mpci_, prec))
+            raise ValueError
+        return g
+
+    @classmethod
+    def _wrap_specfun(cls, name, f, wrap):
+        if wrap:
+            def f_wrapped(ctx, *args, **kwargs):
+                convert = ctx.convert
+                args = [convert(a) for a in args]
+                prec = ctx.prec
+                try:
+                    ctx.prec += 10
+                    retval = f(ctx, *args, **kwargs)
+                finally:
+                    ctx.prec = prec
+                return +retval
+        else:
+            f_wrapped = f
+        setattr(cls, name, f_wrapped)
+
+    def _set_prec(ctx, n):
+        ctx._prec[0] = max(1, int(n))
+        ctx._dps = prec_to_dps(n)
+
+    def _set_dps(ctx, n):
+        ctx._prec[0] = dps_to_prec(n)
+        ctx._dps = max(1, int(n))
+
+    prec = property(lambda ctx: ctx._prec[0], _set_prec)
+    dps = property(lambda ctx: ctx._dps, _set_dps)
+
+    def make_mpf(ctx, v):
+        a = new(ctx.mpf)
+        a._mpi_ = v
+        return a
+
+    def make_mpc(ctx, v):
+        a = new(ctx.mpc)
+        a._mpci_ = v
+        return a
+
+    def _mpq(ctx, pq):
+        p, q = pq
+        a = libmp.from_rational(p, q, ctx.prec, round_floor)
+        b = libmp.from_rational(p, q, ctx.prec, round_ceiling)
+        return ctx.make_mpf((a, b))
+
+    def convert(ctx, x):
+        if isinstance(x, (ctx.mpf, ctx.mpc)):
+            return x
+        if isinstance(x, ctx._constant):
+            return +x
+        if isinstance(x, complex) or hasattr(x, "_mpc_"):
+            re = ctx.convert(x.real)
+            im = ctx.convert(x.imag)
+            return ctx.mpc(re,im)
+        if isinstance(x, basestring):
+            v = mpi_from_str(x, ctx.prec)
+            return ctx.make_mpf(v)
+        if hasattr(x, "_mpi_"):
+            a, b = x._mpi_
+        else:
+            try:
+                a, b = x
+            except (TypeError, ValueError):
+                a = b = x
+            if hasattr(a, "_mpi_"):
+                a = a._mpi_[0]
+            else:
+                a = convert_mpf_(a, ctx.prec, round_floor)
+            if hasattr(b, "_mpi_"):
+                b = b._mpi_[1]
+            else:
+                b = convert_mpf_(b, ctx.prec, round_ceiling)
+        if a == fnan or b == fnan:
+            a = fninf
+            b = finf
+        assert mpf_le(a, b), "endpoints must be properly ordered"
+        return ctx.make_mpf((a, b))
+
+    def nstr(ctx, x, n=5, **kwargs):
+        x = ctx.convert(x)
+        if hasattr(x, "_mpi_"):
+            return libmp.mpi_to_str(x._mpi_, n, **kwargs)
+        if hasattr(x, "_mpci_"):
+            re = libmp.mpi_to_str(x._mpci_[0], n, **kwargs)
+            im = libmp.mpi_to_str(x._mpci_[1], n, **kwargs)
+            return "(%s + %s*j)" % (re, im)
+
+    def mag(ctx, x):
+        x = ctx.convert(x)
+        if isinstance(x, ctx.mpc):
+            return max(ctx.mag(x.real), ctx.mag(x.imag)) + 1
+        a, b = libmp.mpi_abs(x._mpi_)
+        sign, man, exp, bc = b
+        if man:
+            return exp+bc
+        if b == fzero:
+            return ctx.ninf
+        if b == fnan:
+            return ctx.nan
+        return ctx.inf
+
+    def isnan(ctx, x):
+        return False
+
+    def isinf(ctx, x):
+        return x == ctx.inf
+
+    def isint(ctx, x):
+        x = ctx.convert(x)
+        a, b = x._mpi_
+        if a == b:
+            sign, man, exp, bc = a
+            if man:
+                return exp >= 0
+            return a == fzero
+        return None
+
+    def ldexp(ctx, x, n):
+        a, b = ctx.convert(x)._mpi_
+        a = libmp.mpf_shift(a, n)
+        b = libmp.mpf_shift(b, n)
+        return ctx.make_mpf((a,b))
+
+    def absmin(ctx, x):
+        return abs(ctx.convert(x)).a
+
+    def absmax(ctx, x):
+        return abs(ctx.convert(x)).b
+
+    def atan2(ctx, y, x):
+        y = ctx.convert(y)._mpi_
+        x = ctx.convert(x)._mpi_
+        return ctx.make_mpf(libmp.mpi_atan2(y,x,ctx.prec))
+
+    def _convert_param(ctx, x):
+        if isinstance(x, libmp.int_types):
+            return x, 'Z'
+        if isinstance(x, tuple):
+            p, q = x
+            return (ctx.mpf(p) / ctx.mpf(q), 'R')
+        x = ctx.convert(x)
+        if isinstance(x, ctx.mpf):
+            return x, 'R'
+        if isinstance(x, ctx.mpc):
+            return x, 'C'
+        raise ValueError
+
+    def _is_real_type(ctx, z):
+        return isinstance(z, ctx.mpf) or isinstance(z, int_types)
+
+    def _is_complex_type(ctx, z):
+        return isinstance(z, ctx.mpc)
+
+    def hypsum(ctx, p, q, types, coeffs, z, maxterms=6000, **kwargs):
+        coeffs = list(coeffs)
+        num = range(p)
+        den = range(p,p+q)
+        #tol = ctx.eps
+        s = t = ctx.one
+        k = 0
+        while 1:
+            for i in num: t *= (coeffs[i]+k)
+            for i in den: t /= (coeffs[i]+k)
+            k += 1; t /= k; t *= z; s += t
+            if t == 0:
+                return s
+            #if abs(t) < tol:
+            #    return s
+            if k > maxterms:
+                raise ctx.NoConvergence
+
+
+# Register with "numbers" ABC
+#     We do not subclass, hence we do not use the @abstractmethod checks. While
+#     this is less invasive it may turn out that we do not actually support
+#     parts of the expected interfaces.  See
+#     http://docs.python.org/2/library/numbers.html for list of abstract
+#     methods.
+try:
+    import numbers
+    numbers.Complex.register(ivmpc)
+    numbers.Real.register(ivmpf)
+except ImportError:
+    pass

venv/lib/python3.10/site-packages/mpmath/ctx_mp.py

@@ -0,0 +1,1339 @@
+"""
+This module defines the mpf, mpc classes, and standard functions for
+operating with them.
+"""
+__docformat__ = 'plaintext'
+
+import functools
+
+import re
+
+from .ctx_base import StandardBaseContext
+
+from .libmp.backend import basestring, BACKEND
+
+from . import libmp
+
+from .libmp import (MPZ, MPZ_ZERO, MPZ_ONE, int_types, repr_dps,
+    round_floor, round_ceiling, dps_to_prec, round_nearest, prec_to_dps,
+    ComplexResult, to_pickable, from_pickable, normalize,
+    from_int, from_float, from_str, to_int, to_float, to_str,
+    from_rational, from_man_exp,
+    fone, fzero, finf, fninf, fnan,
+    mpf_abs, mpf_pos, mpf_neg, mpf_add, mpf_sub, mpf_mul, mpf_mul_int,
+    mpf_div, mpf_rdiv_int, mpf_pow_int, mpf_mod,
+    mpf_eq, mpf_cmp, mpf_lt, mpf_gt, mpf_le, mpf_ge,
+    mpf_hash, mpf_rand,
+    mpf_sum,
+    bitcount, to_fixed,
+    mpc_to_str,
+    mpc_to_complex, mpc_hash, mpc_pos, mpc_is_nonzero, mpc_neg, mpc_conjugate,
+    mpc_abs, mpc_add, mpc_add_mpf, mpc_sub, mpc_sub_mpf, mpc_mul, mpc_mul_mpf,
+    mpc_mul_int, mpc_div, mpc_div_mpf, mpc_pow, mpc_pow_mpf, mpc_pow_int,
+    mpc_mpf_div,
+    mpf_pow,
+    mpf_pi, mpf_degree, mpf_e, mpf_phi, mpf_ln2, mpf_ln10,
+    mpf_euler, mpf_catalan, mpf_apery, mpf_khinchin,
+    mpf_glaisher, mpf_twinprime, mpf_mertens,
+    int_types)
+
+from . import function_docs
+from . import rational
+
+new = object.__new__
+
+get_complex = re.compile(r'^\(?(?P<re>[\+\-]?\d*(\.\d*)?(e[\+\-]?\d+)?)??'
+                         r'(?P<im>[\+\-]?\d*(\.\d*)?(e[\+\-]?\d+)?j)?\)?$')
+
+if BACKEND == 'sage':
+    from sage.libs.mpmath.ext_main import Context as BaseMPContext
+    # pickle hack
+    import sage.libs.mpmath.ext_main as _mpf_module
+else:
+    from .ctx_mp_python import PythonMPContext as BaseMPContext
+    from . import ctx_mp_python as _mpf_module
+
+from .ctx_mp_python import _mpf, _mpc, mpnumeric
+
+class MPContext(BaseMPContext, StandardBaseContext):
+    """
+    Context for multiprecision arithmetic with a global precision.
+    """
+
+    def __init__(ctx):
+        BaseMPContext.__init__(ctx)
+        ctx.trap_complex = False
+        ctx.pretty = False
+        ctx.types = [ctx.mpf, ctx.mpc, ctx.constant]
+        ctx._mpq = rational.mpq
+        ctx.default()
+        StandardBaseContext.__init__(ctx)
+
+        ctx.mpq = rational.mpq
+        ctx.init_builtins()
+
+        ctx.hyp_summators = {}
+
+        ctx._init_aliases()
+
+        # XXX: automate
+        try:
+            ctx.bernoulli.im_func.func_doc = function_docs.bernoulli
+            ctx.primepi.im_func.func_doc = function_docs.primepi
+            ctx.psi.im_func.func_doc = function_docs.psi
+            ctx.atan2.im_func.func_doc = function_docs.atan2
+        except AttributeError:
+            # python 3
+            ctx.bernoulli.__func__.func_doc = function_docs.bernoulli
+            ctx.primepi.__func__.func_doc = function_docs.primepi
+            ctx.psi.__func__.func_doc = function_docs.psi
+            ctx.atan2.__func__.func_doc = function_docs.atan2
+
+        ctx.digamma.func_doc = function_docs.digamma
+        ctx.cospi.func_doc = function_docs.cospi
+        ctx.sinpi.func_doc = function_docs.sinpi
+
+    def init_builtins(ctx):
+
+        mpf = ctx.mpf
+        mpc = ctx.mpc
+
+        # Exact constants
+        ctx.one = ctx.make_mpf(fone)
+        ctx.zero = ctx.make_mpf(fzero)
+        ctx.j = ctx.make_mpc((fzero,fone))
+        ctx.inf = ctx.make_mpf(finf)
+        ctx.ninf = ctx.make_mpf(fninf)
+        ctx.nan = ctx.make_mpf(fnan)
+
+        eps = ctx.constant(lambda prec, rnd: (0, MPZ_ONE, 1-prec, 1),
+            "epsilon of working precision", "eps")
+        ctx.eps = eps
+
+        # Approximate constants
+        ctx.pi = ctx.constant(mpf_pi, "pi", "pi")
+        ctx.ln2 = ctx.constant(mpf_ln2, "ln(2)", "ln2")
+        ctx.ln10 = ctx.constant(mpf_ln10, "ln(10)", "ln10")
+        ctx.phi = ctx.constant(mpf_phi, "Golden ratio phi", "phi")
+        ctx.e = ctx.constant(mpf_e, "e = exp(1)", "e")
+        ctx.euler = ctx.constant(mpf_euler, "Euler's constant", "euler")
+        ctx.catalan = ctx.constant(mpf_catalan, "Catalan's constant", "catalan")
+        ctx.khinchin = ctx.constant(mpf_khinchin, "Khinchin's constant", "khinchin")
+        ctx.glaisher = ctx.constant(mpf_glaisher, "Glaisher's constant", "glaisher")
+        ctx.apery = ctx.constant(mpf_apery, "Apery's constant", "apery")
+        ctx.degree = ctx.constant(mpf_degree, "1 deg = pi / 180", "degree")
+        ctx.twinprime = ctx.constant(mpf_twinprime, "Twin prime constant", "twinprime")
+        ctx.mertens = ctx.constant(mpf_mertens, "Mertens' constant", "mertens")
+
+        # Standard functions
+        ctx.sqrt = ctx._wrap_libmp_function(libmp.mpf_sqrt, libmp.mpc_sqrt)
+        ctx.cbrt = ctx._wrap_libmp_function(libmp.mpf_cbrt, libmp.mpc_cbrt)
+        ctx.ln = ctx._wrap_libmp_function(libmp.mpf_log, libmp.mpc_log)
+        ctx.atan = ctx._wrap_libmp_function(libmp.mpf_atan, libmp.mpc_atan)
+        ctx.exp = ctx._wrap_libmp_function(libmp.mpf_exp, libmp.mpc_exp)
+        ctx.expj = ctx._wrap_libmp_function(libmp.mpf_expj, libmp.mpc_expj)
+        ctx.expjpi = ctx._wrap_libmp_function(libmp.mpf_expjpi, libmp.mpc_expjpi)
+        ctx.sin = ctx._wrap_libmp_function(libmp.mpf_sin, libmp.mpc_sin)
+        ctx.cos = ctx._wrap_libmp_function(libmp.mpf_cos, libmp.mpc_cos)
+        ctx.tan = ctx._wrap_libmp_function(libmp.mpf_tan, libmp.mpc_tan)
+        ctx.sinh = ctx._wrap_libmp_function(libmp.mpf_sinh, libmp.mpc_sinh)
+        ctx.cosh = ctx._wrap_libmp_function(libmp.mpf_cosh, libmp.mpc_cosh)
+        ctx.tanh = ctx._wrap_libmp_function(libmp.mpf_tanh, libmp.mpc_tanh)
+        ctx.asin = ctx._wrap_libmp_function(libmp.mpf_asin, libmp.mpc_asin)
+        ctx.acos = ctx._wrap_libmp_function(libmp.mpf_acos, libmp.mpc_acos)
+        ctx.atan = ctx._wrap_libmp_function(libmp.mpf_atan, libmp.mpc_atan)
+        ctx.asinh = ctx._wrap_libmp_function(libmp.mpf_asinh, libmp.mpc_asinh)
+        ctx.acosh = ctx._wrap_libmp_function(libmp.mpf_acosh, libmp.mpc_acosh)
+        ctx.atanh = ctx._wrap_libmp_function(libmp.mpf_atanh, libmp.mpc_atanh)
+        ctx.sinpi = ctx._wrap_libmp_function(libmp.mpf_sin_pi, libmp.mpc_sin_pi)
+        ctx.cospi = ctx._wrap_libmp_function(libmp.mpf_cos_pi, libmp.mpc_cos_pi)
+        ctx.floor = ctx._wrap_libmp_function(libmp.mpf_floor, libmp.mpc_floor)
+        ctx.ceil = ctx._wrap_libmp_function(libmp.mpf_ceil, libmp.mpc_ceil)
+        ctx.nint = ctx._wrap_libmp_function(libmp.mpf_nint, libmp.mpc_nint)
+        ctx.frac = ctx._wrap_libmp_function(libmp.mpf_frac, libmp.mpc_frac)
+        ctx.fib = ctx.fibonacci = ctx._wrap_libmp_function(libmp.mpf_fibonacci, libmp.mpc_fibonacci)
+
+        ctx.gamma = ctx._wrap_libmp_function(libmp.mpf_gamma, libmp.mpc_gamma)
+        ctx.rgamma = ctx._wrap_libmp_function(libmp.mpf_rgamma, libmp.mpc_rgamma)
+        ctx.loggamma = ctx._wrap_libmp_function(libmp.mpf_loggamma, libmp.mpc_loggamma)
+        ctx.fac = ctx.factorial = ctx._wrap_libmp_function(libmp.mpf_factorial, libmp.mpc_factorial)
+
+        ctx.digamma = ctx._wrap_libmp_function(libmp.mpf_psi0, libmp.mpc_psi0)
+        ctx.harmonic = ctx._wrap_libmp_function(libmp.mpf_harmonic, libmp.mpc_harmonic)
+        ctx.ei = ctx._wrap_libmp_function(libmp.mpf_ei, libmp.mpc_ei)
+        ctx.e1 = ctx._wrap_libmp_function(libmp.mpf_e1, libmp.mpc_e1)
+        ctx._ci = ctx._wrap_libmp_function(libmp.mpf_ci, libmp.mpc_ci)
+        ctx._si = ctx._wrap_libmp_function(libmp.mpf_si, libmp.mpc_si)
+        ctx.ellipk = ctx._wrap_libmp_function(libmp.mpf_ellipk, libmp.mpc_ellipk)
+        ctx._ellipe = ctx._wrap_libmp_function(libmp.mpf_ellipe, libmp.mpc_ellipe)
+        ctx.agm1 = ctx._wrap_libmp_function(libmp.mpf_agm1, libmp.mpc_agm1)
+        ctx._erf = ctx._wrap_libmp_function(libmp.mpf_erf, None)
+        ctx._erfc = ctx._wrap_libmp_function(libmp.mpf_erfc, None)
+        ctx._zeta = ctx._wrap_libmp_function(libmp.mpf_zeta, libmp.mpc_zeta)
+        ctx._altzeta = ctx._wrap_libmp_function(libmp.mpf_altzeta, libmp.mpc_altzeta)
+
+        # Faster versions
+        ctx.sqrt = getattr(ctx, "_sage_sqrt", ctx.sqrt)
+        ctx.exp = getattr(ctx, "_sage_exp", ctx.exp)
+        ctx.ln = getattr(ctx, "_sage_ln", ctx.ln)
+        ctx.cos = getattr(ctx, "_sage_cos", ctx.cos)
+        ctx.sin = getattr(ctx, "_sage_sin", ctx.sin)
+
+    def to_fixed(ctx, x, prec):
+        return x.to_fixed(prec)
+
+    def hypot(ctx, x, y):
+        r"""
+        Computes the Euclidean norm of the vector `(x, y)`, equal
+        to `\sqrt{x^2 + y^2}`. Both `x` and `y` must be real."""
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        return ctx.make_mpf(libmp.mpf_hypot(x._mpf_, y._mpf_, *ctx._prec_rounding))
+
+    def _gamma_upper_int(ctx, n, z):
+        n = int(ctx._re(n))
+        if n == 0:
+            return ctx.e1(z)
+        if not hasattr(z, '_mpf_'):
+            raise NotImplementedError
+        prec, rounding = ctx._prec_rounding
+        real, imag = libmp.mpf_expint(n, z._mpf_, prec, rounding, gamma=True)
+        if imag is None:
+            return ctx.make_mpf(real)
+        else:
+            return ctx.make_mpc((real, imag))
+
+    def _expint_int(ctx, n, z):
+        n = int(n)
+        if n == 1:
+            return ctx.e1(z)
+        if not hasattr(z, '_mpf_'):
+            raise NotImplementedError
+        prec, rounding = ctx._prec_rounding
+        real, imag = libmp.mpf_expint(n, z._mpf_, prec, rounding)
+        if imag is None:
+            return ctx.make_mpf(real)
+        else:
+            return ctx.make_mpc((real, imag))
+
+    def _nthroot(ctx, x, n):
+        if hasattr(x, '_mpf_'):
+            try:
+                return ctx.make_mpf(libmp.mpf_nthroot(x._mpf_, n, *ctx._prec_rounding))
+            except ComplexResult:
+                if ctx.trap_complex:
+                    raise
+                x = (x._mpf_, libmp.fzero)
+        else:
+            x = x._mpc_
+        return ctx.make_mpc(libmp.mpc_nthroot(x, n, *ctx._prec_rounding))
+
+    def _besselj(ctx, n, z):
+        prec, rounding = ctx._prec_rounding
+        if hasattr(z, '_mpf_'):
+            return ctx.make_mpf(libmp.mpf_besseljn(n, z._mpf_, prec, rounding))
+        elif hasattr(z, '_mpc_'):
+            return ctx.make_mpc(libmp.mpc_besseljn(n, z._mpc_, prec, rounding))
+
+    def _agm(ctx, a, b=1):
+        prec, rounding = ctx._prec_rounding
+        if hasattr(a, '_mpf_') and hasattr(b, '_mpf_'):
+            try:
+                v = libmp.mpf_agm(a._mpf_, b._mpf_, prec, rounding)
+                return ctx.make_mpf(v)
+            except ComplexResult:
+                pass
+        if hasattr(a, '_mpf_'): a = (a._mpf_, libmp.fzero)
+        else: a = a._mpc_
+        if hasattr(b, '_mpf_'): b = (b._mpf_, libmp.fzero)
+        else: b = b._mpc_
+        return ctx.make_mpc(libmp.mpc_agm(a, b, prec, rounding))
+
+    def bernoulli(ctx, n):
+        return ctx.make_mpf(libmp.mpf_bernoulli(int(n), *ctx._prec_rounding))
+
+    def _zeta_int(ctx, n):
+        return ctx.make_mpf(libmp.mpf_zeta_int(int(n), *ctx._prec_rounding))
+
+    def atan2(ctx, y, x):
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        return ctx.make_mpf(libmp.mpf_atan2(y._mpf_, x._mpf_, *ctx._prec_rounding))
+
+    def psi(ctx, m, z):
+        z = ctx.convert(z)
+        m = int(m)
+        if ctx._is_real_type(z):
+            return ctx.make_mpf(libmp.mpf_psi(m, z._mpf_, *ctx._prec_rounding))
+        else:
+            return ctx.make_mpc(libmp.mpc_psi(m, z._mpc_, *ctx._prec_rounding))
+
+    def cos_sin(ctx, x, **kwargs):
+        if type(x) not in ctx.types:
+            x = ctx.convert(x)
+        prec, rounding = ctx._parse_prec(kwargs)
+        if hasattr(x, '_mpf_'):
+            c, s = libmp.mpf_cos_sin(x._mpf_, prec, rounding)
+            return ctx.make_mpf(c), ctx.make_mpf(s)
+        elif hasattr(x, '_mpc_'):
+            c, s = libmp.mpc_cos_sin(x._mpc_, prec, rounding)
+            return ctx.make_mpc(c), ctx.make_mpc(s)
+        else:
+            return ctx.cos(x, **kwargs), ctx.sin(x, **kwargs)
+
+    def cospi_sinpi(ctx, x, **kwargs):
+        if type(x) not in ctx.types:
+            x = ctx.convert(x)
+        prec, rounding = ctx._parse_prec(kwargs)
+        if hasattr(x, '_mpf_'):
+            c, s = libmp.mpf_cos_sin_pi(x._mpf_, prec, rounding)
+            return ctx.make_mpf(c), ctx.make_mpf(s)
+        elif hasattr(x, '_mpc_'):
+            c, s = libmp.mpc_cos_sin_pi(x._mpc_, prec, rounding)
+            return ctx.make_mpc(c), ctx.make_mpc(s)
+        else:
+            return ctx.cos(x, **kwargs), ctx.sin(x, **kwargs)
+
+    def clone(ctx):
+        """
+        Create a copy of the context, with the same working precision.
+        """
+        a = ctx.__class__()
+        a.prec = ctx.prec
+        return a
+
+    # Several helper methods
+    # TODO: add more of these, make consistent, write docstrings, ...
+
+    def _is_real_type(ctx, x):
+        if hasattr(x, '_mpc_') or type(x) is complex:
+            return False
+        return True
+
+    def _is_complex_type(ctx, x):
+        if hasattr(x, '_mpc_') or type(x) is complex:
+            return True
+        return False
+
+    def isnan(ctx, x):
+        """
+        Return *True* if *x* is a NaN (not-a-number), or for a complex
+        number, whether either the real or complex part is NaN;
+        otherwise return *False*::
+
+            >>> from mpmath import *
+            >>> isnan(3.14)
+            False
+            >>> isnan(nan)
+            True
+            >>> isnan(mpc(3.14,2.72))
+            False
+            >>> isnan(mpc(3.14,nan))
+            True
+
+        """
+        if hasattr(x, "_mpf_"):
+            return x._mpf_ == fnan
+        if hasattr(x, "_mpc_"):
+            return fnan in x._mpc_
+        if isinstance(x, int_types) or isinstance(x, rational.mpq):
+            return False
+        x = ctx.convert(x)
+        if hasattr(x, '_mpf_') or hasattr(x, '_mpc_'):
+            return ctx.isnan(x)
+        raise TypeError("isnan() needs a number as input")
+
+    def isfinite(ctx, x):
+        """
+        Return *True* if *x* is a finite number, i.e. neither
+        an infinity or a NaN.
+
+            >>> from mpmath import *
+            >>> isfinite(inf)
+            False
+            >>> isfinite(-inf)
+            False
+            >>> isfinite(3)
+            True
+            >>> isfinite(nan)
+            False
+            >>> isfinite(3+4j)
+            True
+            >>> isfinite(mpc(3,inf))
+            False
+            >>> isfinite(mpc(nan,3))
+            False
+
+        """
+        if ctx.isinf(x) or ctx.isnan(x):
+            return False
+        return True
+
+    def isnpint(ctx, x):
+        """
+        Determine if *x* is a nonpositive integer.
+        """
+        if not x:
+            return True
+        if hasattr(x, '_mpf_'):
+            sign, man, exp, bc = x._mpf_
+            return sign and exp >= 0
+        if hasattr(x, '_mpc_'):
+            return not x.imag and ctx.isnpint(x.real)
+        if type(x) in int_types:
+            return x <= 0
+        if isinstance(x, ctx.mpq):
+            p, q = x._mpq_
+            if not p:
+                return True
+            return q == 1 and p <= 0
+        return ctx.isnpint(ctx.convert(x))
+
+    def __str__(ctx):
+        lines = ["Mpmath settings:",
+            ("  mp.prec = %s" % ctx.prec).ljust(30) + "[default: 53]",
+            ("  mp.dps = %s" % ctx.dps).ljust(30) + "[default: 15]",
+            ("  mp.trap_complex = %s" % ctx.trap_complex).ljust(30) + "[default: False]",
+        ]
+        return "\n".join(lines)
+
+    @property
+    def _repr_digits(ctx):
+        return repr_dps(ctx._prec)
+
+    @property
+    def _str_digits(ctx):
+        return ctx._dps
+
+    def extraprec(ctx, n, normalize_output=False):
+        """
+        The block
+
+            with extraprec(n):
+                <code>
+
+        increases the precision n bits, executes <code>, and then
+        restores the precision.
+
+        extraprec(n)(f) returns a decorated version of the function f
+        that increases the working precision by n bits before execution,
+        and restores the parent precision afterwards. With
+        normalize_output=True, it rounds the return value to the parent
+        precision.
+        """
+        return PrecisionManager(ctx, lambda p: p + n, None, normalize_output)
+
+    def extradps(ctx, n, normalize_output=False):
+        """
+        This function is analogous to extraprec (see documentation)
+        but changes the decimal precision instead of the number of bits.
+        """
+        return PrecisionManager(ctx, None, lambda d: d + n, normalize_output)
+
+    def workprec(ctx, n, normalize_output=False):
+        """
+        The block
+
+            with workprec(n):
+                <code>
+
+        sets the precision to n bits, executes <code>, and then restores
+        the precision.
+
+        workprec(n)(f) returns a decorated version of the function f
+        that sets the precision to n bits before execution,
+        and restores the precision afterwards. With normalize_output=True,
+        it rounds the return value to the parent precision.
+        """
+        return PrecisionManager(ctx, lambda p: n, None, normalize_output)
+
+    def workdps(ctx, n, normalize_output=False):
+        """
+        This function is analogous to workprec (see documentation)
+        but changes the decimal precision instead of the number of bits.
+        """
+        return PrecisionManager(ctx, None, lambda d: n, normalize_output)
+
+    def autoprec(ctx, f, maxprec=None, catch=(), verbose=False):
+        r"""
+        Return a wrapped copy of *f* that repeatedly evaluates *f*
+        with increasing precision until the result converges to the
+        full precision used at the point of the call.
+
+        This heuristically protects against rounding errors, at the cost of
+        roughly a 2x slowdown compared to manually setting the optimal
+        precision. This method can, however, easily be fooled if the results
+        from *f* depend "discontinuously" on the precision, for instance
+        if catastrophic cancellation can occur. Therefore, :func:`~mpmath.autoprec`
+        should be used judiciously.
+
+        **Examples**
+
+        Many functions are sensitive to perturbations of the input arguments.
+        If the arguments are decimal numbers, they may have to be converted
+        to binary at a much higher precision. If the amount of required
+        extra precision is unknown, :func:`~mpmath.autoprec` is convenient::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15
+            >>> mp.pretty = True
+            >>> besselj(5, 125 * 10**28)    # Exact input
+            -8.03284785591801e-17
+            >>> besselj(5, '1.25e30')   # Bad
+            7.12954868316652e-16
+            >>> autoprec(besselj)(5, '1.25e30')   # Good
+            -8.03284785591801e-17
+
+        The following fails to converge because `\sin(\pi) = 0` whereas all
+        finite-precision approximations of `\pi` give nonzero values::
+
+            >>> autoprec(sin)(pi) # doctest: +IGNORE_EXCEPTION_DETAIL
+            Traceback (most recent call last):
+              ...
+            NoConvergence: autoprec: prec increased to 2910 without convergence
+
+        As the following example shows, :func:`~mpmath.autoprec` can protect against
+        cancellation, but is fooled by too severe cancellation::
+
+            >>> x = 1e-10
+            >>> exp(x)-1; expm1(x); autoprec(lambda t: exp(t)-1)(x)
+            1.00000008274037e-10
+            1.00000000005e-10
+            1.00000000005e-10
+            >>> x = 1e-50
+            >>> exp(x)-1; expm1(x); autoprec(lambda t: exp(t)-1)(x)
+            0.0
+            1.0e-50
+            0.0
+
+        With *catch*, an exception or list of exceptions to intercept
+        may be specified. The raised exception is interpreted
+        as signaling insufficient precision. This permits, for example,
+        evaluating a function where a too low precision results in a
+        division by zero::
+
+            >>> f = lambda x: 1/(exp(x)-1)
+            >>> f(1e-30)
+            Traceback (most recent call last):
+              ...
+            ZeroDivisionError
+            >>> autoprec(f, catch=ZeroDivisionError)(1e-30)
+            1.0e+30
+
+
+        """
+        def f_autoprec_wrapped(*args, **kwargs):
+            prec = ctx.prec
+            if maxprec is None:
+                maxprec2 = ctx._default_hyper_maxprec(prec)
+            else:
+                maxprec2 = maxprec
+            try:
+                ctx.prec = prec + 10
+                try:
+                    v1 = f(*args, **kwargs)
+                except catch:
+                    v1 = ctx.nan
+                prec2 = prec + 20
+                while 1:
+                    ctx.prec = prec2
+                    try:
+                        v2 = f(*args, **kwargs)
+                    except catch:
+                        v2 = ctx.nan
+                    if v1 == v2:
+                        break
+                    err = ctx.mag(v2-v1) - ctx.mag(v2)
+                    if err < (-prec):
+                        break
+                    if verbose:
+                        print("autoprec: target=%s, prec=%s, accuracy=%s" \
+                            % (prec, prec2, -err))
+                    v1 = v2
+                    if prec2 >= maxprec2:
+                        raise ctx.NoConvergence(\
+                        "autoprec: prec increased to %i without convergence"\
+                        % prec2)
+                    prec2 += int(prec2*2)
+                    prec2 = min(prec2, maxprec2)
+            finally:
+                ctx.prec = prec
+            return +v2
+        return f_autoprec_wrapped
+
+    def nstr(ctx, x, n=6, **kwargs):
+        """
+        Convert an ``mpf`` or ``mpc`` to a decimal string literal with *n*
+        significant digits. The small default value for *n* is chosen to
+        make this function useful for printing collections of numbers
+        (lists, matrices, etc).
+
+        If *x* is a list or tuple, :func:`~mpmath.nstr` is applied recursively
+        to each element. For unrecognized classes, :func:`~mpmath.nstr`
+        simply returns ``str(x)``.
+
+        The companion function :func:`~mpmath.nprint` prints the result
+        instead of returning it.
+
+        The keyword arguments *strip_zeros*, *min_fixed*, *max_fixed*
+        and *show_zero_exponent* are forwarded to :func:`~mpmath.libmp.to_str`.
+
+        The number will be printed in fixed-point format if the position
+        of the leading digit is strictly between min_fixed
+        (default = min(-dps/3,-5)) and max_fixed (default = dps).
+
+        To force fixed-point format always, set min_fixed = -inf,
+        max_fixed = +inf. To force floating-point format, set
+        min_fixed >= max_fixed.
+
+            >>> from mpmath import *
+            >>> nstr([+pi, ldexp(1,-500)])
+            '[3.14159, 3.05494e-151]'
+            >>> nprint([+pi, ldexp(1,-500)])
+            [3.14159, 3.05494e-151]
+            >>> nstr(mpf("5e-10"), 5)
+            '5.0e-10'
+            >>> nstr(mpf("5e-10"), 5, strip_zeros=False)
+            '5.0000e-10'
+            >>> nstr(mpf("5e-10"), 5, strip_zeros=False, min_fixed=-11)
+            '0.00000000050000'
+            >>> nstr(mpf(0), 5, show_zero_exponent=True)
+            '0.0e+0'
+
+        """
+        if isinstance(x, list):
+            return "[%s]" % (", ".join(ctx.nstr(c, n, **kwargs) for c in x))
+        if isinstance(x, tuple):
+            return "(%s)" % (", ".join(ctx.nstr(c, n, **kwargs) for c in x))
+        if hasattr(x, '_mpf_'):
+            return to_str(x._mpf_, n, **kwargs)
+        if hasattr(x, '_mpc_'):
+            return "(" + mpc_to_str(x._mpc_, n, **kwargs)  + ")"
+        if isinstance(x, basestring):
+            return repr(x)
+        if isinstance(x, ctx.matrix):
+            return x.__nstr__(n, **kwargs)
+        return str(x)
+
+    def _convert_fallback(ctx, x, strings):
+        if strings and isinstance(x, basestring):
+            if 'j' in x.lower():
+                x = x.lower().replace(' ', '')
+                match = get_complex.match(x)
+                re = match.group('re')
+                if not re:
+                    re = 0
+                im = match.group('im').rstrip('j')
+                return ctx.mpc(ctx.convert(re), ctx.convert(im))
+        if hasattr(x, "_mpi_"):
+            a, b = x._mpi_
+            if a == b:
+                return ctx.make_mpf(a)
+            else:
+                raise ValueError("can only create mpf from zero-width interval")
+        raise TypeError("cannot create mpf from " + repr(x))
+
+    def mpmathify(ctx, *args, **kwargs):
+        return ctx.convert(*args, **kwargs)
+
+    def _parse_prec(ctx, kwargs):
+        if kwargs:
+            if kwargs.get('exact'):
+                return 0, 'f'
+            prec, rounding = ctx._prec_rounding
+            if 'rounding' in kwargs:
+                rounding = kwargs['rounding']
+            if 'prec' in kwargs:
+                prec = kwargs['prec']
+                if prec == ctx.inf:
+                    return 0, 'f'
+                else:
+                    prec = int(prec)
+            elif 'dps' in kwargs:
+                dps = kwargs['dps']
+                if dps == ctx.inf:
+                    return 0, 'f'
+                prec = dps_to_prec(dps)
+            return prec, rounding
+        return ctx._prec_rounding
+
+    _exact_overflow_msg = "the exact result does not fit in memory"
+
+    _hypsum_msg = """hypsum() failed to converge to the requested %i bits of accuracy
+using a working precision of %i bits. Try with a higher maxprec,
+maxterms, or set zeroprec."""
+
+    def hypsum(ctx, p, q, flags, coeffs, z, accurate_small=True, **kwargs):
+        if hasattr(z, "_mpf_"):
+            key = p, q, flags, 'R'
+            v = z._mpf_
+        elif hasattr(z, "_mpc_"):
+            key = p, q, flags, 'C'
+            v = z._mpc_
+        if key not in ctx.hyp_summators:
+            ctx.hyp_summators[key] = libmp.make_hyp_summator(key)[1]
+        summator = ctx.hyp_summators[key]
+        prec = ctx.prec
+        maxprec = kwargs.get('maxprec', ctx._default_hyper_maxprec(prec))
+        extraprec = 50
+        epsshift = 25
+        # Jumps in magnitude occur when parameters are close to negative
+        # integers. We must ensure that these terms are included in
+        # the sum and added accurately
+        magnitude_check = {}
+        max_total_jump = 0
+        for i, c in enumerate(coeffs):
+            if flags[i] == 'Z':
+                if i >= p and c <= 0:
+                    ok = False
+                    for ii, cc in enumerate(coeffs[:p]):
+                        # Note: c <= cc or c < cc, depending on convention
+                        if flags[ii] == 'Z' and cc <= 0 and c <= cc:
+                            ok = True
+                    if not ok:
+                        raise ZeroDivisionError("pole in hypergeometric series")
+                continue
+            n, d = ctx.nint_distance(c)
+            n = -int(n)
+            d = -d
+            if i >= p and n >= 0 and d > 4:
+                if n in magnitude_check:
+                    magnitude_check[n] += d
+                else:
+                    magnitude_check[n] = d
+                extraprec = max(extraprec, d - prec + 60)
+            max_total_jump += abs(d)
+        while 1:
+            if extraprec > maxprec:
+                raise ValueError(ctx._hypsum_msg % (prec, prec+extraprec))
+            wp = prec + extraprec
+            if magnitude_check:
+                mag_dict = dict((n,None) for n in magnitude_check)
+            else:
+                mag_dict = {}
+            zv, have_complex, magnitude = summator(coeffs, v, prec, wp, \
+                epsshift, mag_dict, **kwargs)
+            cancel = -magnitude
+            jumps_resolved = True
+            if extraprec < max_total_jump:
+                for n in mag_dict.values():
+                    if (n is None) or (n < prec):
+                        jumps_resolved = False
+                        break
+            accurate = (cancel < extraprec-25-5 or not accurate_small)
+            if jumps_resolved:
+                if accurate:
+                    break
+                # zero?
+                zeroprec = kwargs.get('zeroprec')
+                if zeroprec is not None:
+                    if cancel > zeroprec:
+                        if have_complex:
+                            return ctx.mpc(0)
+                        else:
+                            return ctx.zero
+
+            # Some near-singularities were not included, so increase
+            # precision and repeat until they are
+            extraprec *= 2
+            # Possible workaround for bad roundoff in fixed-point arithmetic
+            epsshift += 5
+            extraprec += 5
+
+        if type(zv) is tuple:
+            if have_complex:
+                return ctx.make_mpc(zv)
+            else:
+                return ctx.make_mpf(zv)
+        else:
+            return zv
+
+    def ldexp(ctx, x, n):
+        r"""
+        Computes `x 2^n` efficiently. No rounding is performed.
+        The argument `x` must be a real floating-point number (or
+        possible to convert into one) and `n` must be a Python ``int``.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> ldexp(1, 10)
+            mpf('1024.0')
+            >>> ldexp(1, -3)
+            mpf('0.125')
+
+        """
+        x = ctx.convert(x)
+        return ctx.make_mpf(libmp.mpf_shift(x._mpf_, n))
+
+    def frexp(ctx, x):
+        r"""
+        Given a real number `x`, returns `(y, n)` with `y \in [0.5, 1)`,
+        `n` a Python integer, and such that `x = y 2^n`. No rounding is
+        performed.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> frexp(7.5)
+            (mpf('0.9375'), 3)
+
+        """
+        x = ctx.convert(x)
+        y, n = libmp.mpf_frexp(x._mpf_)
+        return ctx.make_mpf(y), n
+
+    def fneg(ctx, x, **kwargs):
+        """
+        Negates the number *x*, giving a floating-point result, optionally
+        using a custom precision and rounding mode.
+
+        See the documentation of :func:`~mpmath.fadd` for a detailed description
+        of how to specify precision and rounding.
+
+        **Examples**
+
+        An mpmath number is returned::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fneg(2.5)
+            mpf('-2.5')
+            >>> fneg(-5+2j)
+            mpc(real='5.0', imag='-2.0')
+
+        Precise control over rounding is possible::
+
+            >>> x = fadd(2, 1e-100, exact=True)
+            >>> fneg(x)
+            mpf('-2.0')
+            >>> fneg(x, rounding='f')
+            mpf('-2.0000000000000004')
+
+        Negating with and without roundoff::
+
+            >>> n = 200000000000000000000001
+            >>> print(int(-mpf(n)))
+            -200000000000000016777216
+            >>> print(int(fneg(n)))
+            -200000000000000016777216
+            >>> print(int(fneg(n, prec=log(n,2)+1)))
+            -200000000000000000000001
+            >>> print(int(fneg(n, dps=log(n,10)+1)))
+            -200000000000000000000001
+            >>> print(int(fneg(n, prec=inf)))
+            -200000000000000000000001
+            >>> print(int(fneg(n, dps=inf)))
+            -200000000000000000000001
+            >>> print(int(fneg(n, exact=True)))
+            -200000000000000000000001
+
+        """
+        prec, rounding = ctx._parse_prec(kwargs)
+        x = ctx.convert(x)
+        if hasattr(x, '_mpf_'):
+            return ctx.make_mpf(mpf_neg(x._mpf_, prec, rounding))
+        if hasattr(x, '_mpc_'):
+            return ctx.make_mpc(mpc_neg(x._mpc_, prec, rounding))
+        raise ValueError("Arguments need to be mpf or mpc compatible numbers")
+
+    def fadd(ctx, x, y, **kwargs):
+        """
+        Adds the numbers *x* and *y*, giving a floating-point result,
+        optionally using a custom precision and rounding mode.
+
+        The default precision is the working precision of the context.
+        You can specify a custom precision in bits by passing the *prec* keyword
+        argument, or by providing an equivalent decimal precision with the *dps*
+        keyword argument. If the precision is set to ``+inf``, or if the flag
+        *exact=True* is passed, an exact addition with no rounding is performed.
+
+        When the precision is finite, the optional *rounding* keyword argument
+        specifies the direction of rounding. Valid options are ``'n'`` for
+        nearest (default), ``'f'`` for floor, ``'c'`` for ceiling, ``'d'``
+        for down, ``'u'`` for up.
+
+        **Examples**
+
+        Using :func:`~mpmath.fadd` with precision and rounding control::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fadd(2, 1e-20)
+            mpf('2.0')
+            >>> fadd(2, 1e-20, rounding='u')
+            mpf('2.0000000000000004')
+            >>> nprint(fadd(2, 1e-20, prec=100), 25)
+            2.00000000000000000001
+            >>> nprint(fadd(2, 1e-20, dps=15), 25)
+            2.0
+            >>> nprint(fadd(2, 1e-20, dps=25), 25)
+            2.00000000000000000001
+            >>> nprint(fadd(2, 1e-20, exact=True), 25)
+            2.00000000000000000001
+
+        Exact addition avoids cancellation errors, enforcing familiar laws
+        of numbers such as `x+y-x = y`, which don't hold in floating-point
+        arithmetic with finite precision::
+
+            >>> x, y = mpf(2), mpf('1e-1000')
+            >>> print(x + y - x)
+            0.0
+            >>> print(fadd(x, y, prec=inf) - x)
+            1.0e-1000
+            >>> print(fadd(x, y, exact=True) - x)
+            1.0e-1000
+
+        Exact addition can be inefficient and may be impossible to perform
+        with large magnitude differences::
+
+            >>> fadd(1, '1e-100000000000000000000', prec=inf)
+            Traceback (most recent call last):
+              ...
+            OverflowError: the exact result does not fit in memory
+
+        """
+        prec, rounding = ctx._parse_prec(kwargs)
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        try:
+            if hasattr(x, '_mpf_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpf(mpf_add(x._mpf_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_add_mpf(y._mpc_, x._mpf_, prec, rounding))
+            if hasattr(x, '_mpc_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpc(mpc_add_mpf(x._mpc_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_add(x._mpc_, y._mpc_, prec, rounding))
+        except (ValueError, OverflowError):
+            raise OverflowError(ctx._exact_overflow_msg)
+        raise ValueError("Arguments need to be mpf or mpc compatible numbers")
+
+    def fsub(ctx, x, y, **kwargs):
+        """
+        Subtracts the numbers *x* and *y*, giving a floating-point result,
+        optionally using a custom precision and rounding mode.
+
+        See the documentation of :func:`~mpmath.fadd` for a detailed description
+        of how to specify precision and rounding.
+
+        **Examples**
+
+        Using :func:`~mpmath.fsub` with precision and rounding control::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fsub(2, 1e-20)
+            mpf('2.0')
+            >>> fsub(2, 1e-20, rounding='d')
+            mpf('1.9999999999999998')
+            >>> nprint(fsub(2, 1e-20, prec=100), 25)
+            1.99999999999999999999
+            >>> nprint(fsub(2, 1e-20, dps=15), 25)
+            2.0
+            >>> nprint(fsub(2, 1e-20, dps=25), 25)
+            1.99999999999999999999
+            >>> nprint(fsub(2, 1e-20, exact=True), 25)
+            1.99999999999999999999
+
+        Exact subtraction avoids cancellation errors, enforcing familiar laws
+        of numbers such as `x-y+y = x`, which don't hold in floating-point
+        arithmetic with finite precision::
+
+            >>> x, y = mpf(2), mpf('1e1000')
+            >>> print(x - y + y)
+            0.0
+            >>> print(fsub(x, y, prec=inf) + y)
+            2.0
+            >>> print(fsub(x, y, exact=True) + y)
+            2.0
+
+        Exact addition can be inefficient and may be impossible to perform
+        with large magnitude differences::
+
+            >>> fsub(1, '1e-100000000000000000000', prec=inf)
+            Traceback (most recent call last):
+              ...
+            OverflowError: the exact result does not fit in memory
+
+        """
+        prec, rounding = ctx._parse_prec(kwargs)
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        try:
+            if hasattr(x, '_mpf_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpf(mpf_sub(x._mpf_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_sub((x._mpf_, fzero), y._mpc_, prec, rounding))
+            if hasattr(x, '_mpc_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpc(mpc_sub_mpf(x._mpc_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_sub(x._mpc_, y._mpc_, prec, rounding))
+        except (ValueError, OverflowError):
+            raise OverflowError(ctx._exact_overflow_msg)
+        raise ValueError("Arguments need to be mpf or mpc compatible numbers")
+
+    def fmul(ctx, x, y, **kwargs):
+        """
+        Multiplies the numbers *x* and *y*, giving a floating-point result,
+        optionally using a custom precision and rounding mode.
+
+        See the documentation of :func:`~mpmath.fadd` for a detailed description
+        of how to specify precision and rounding.
+
+        **Examples**
+
+        The result is an mpmath number::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fmul(2, 5.0)
+            mpf('10.0')
+            >>> fmul(0.5j, 0.5)
+            mpc(real='0.0', imag='0.25')
+
+        Avoiding roundoff::
+
+            >>> x, y = 10**10+1, 10**15+1
+            >>> print(x*y)
+            10000000001000010000000001
+            >>> print(mpf(x) * mpf(y))
+            1.0000000001e+25
+            >>> print(int(mpf(x) * mpf(y)))
+            10000000001000011026399232
+            >>> print(int(fmul(x, y)))
+            10000000001000011026399232
+            >>> print(int(fmul(x, y, dps=25)))
+            10000000001000010000000001
+            >>> print(int(fmul(x, y, exact=True)))
+            10000000001000010000000001
+
+        Exact multiplication with complex numbers can be inefficient and may
+        be impossible to perform with large magnitude differences between
+        real and imaginary parts::
+
+            >>> x = 1+2j
+            >>> y = mpc(2, '1e-100000000000000000000')
+            >>> fmul(x, y)
+            mpc(real='2.0', imag='4.0')
+            >>> fmul(x, y, rounding='u')
+            mpc(real='2.0', imag='4.0000000000000009')
+            >>> fmul(x, y, exact=True)
+            Traceback (most recent call last):
+              ...
+            OverflowError: the exact result does not fit in memory
+
+        """
+        prec, rounding = ctx._parse_prec(kwargs)
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        try:
+            if hasattr(x, '_mpf_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpf(mpf_mul(x._mpf_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_mul_mpf(y._mpc_, x._mpf_, prec, rounding))
+            if hasattr(x, '_mpc_'):
+                if hasattr(y, '_mpf_'):
+                    return ctx.make_mpc(mpc_mul_mpf(x._mpc_, y._mpf_, prec, rounding))
+                if hasattr(y, '_mpc_'):
+                    return ctx.make_mpc(mpc_mul(x._mpc_, y._mpc_, prec, rounding))
+        except (ValueError, OverflowError):
+            raise OverflowError(ctx._exact_overflow_msg)
+        raise ValueError("Arguments need to be mpf or mpc compatible numbers")
+
+    def fdiv(ctx, x, y, **kwargs):
+        """
+        Divides the numbers *x* and *y*, giving a floating-point result,
+        optionally using a custom precision and rounding mode.
+
+        See the documentation of :func:`~mpmath.fadd` for a detailed description
+        of how to specify precision and rounding.
+
+        **Examples**
+
+        The result is an mpmath number::
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fdiv(3, 2)
+            mpf('1.5')
+            >>> fdiv(2, 3)
+            mpf('0.66666666666666663')
+            >>> fdiv(2+4j, 0.5)
+            mpc(real='4.0', imag='8.0')
+
+        The rounding direction and precision can be controlled::
+
+            >>> fdiv(2, 3, dps=3)    # Should be accurate to at least 3 digits
+            mpf('0.6666259765625')
+            >>> fdiv(2, 3, rounding='d')
+            mpf('0.66666666666666663')
+            >>> fdiv(2, 3, prec=60)
+            mpf('0.66666666666666667')
+            >>> fdiv(2, 3, rounding='u')
+            mpf('0.66666666666666674')
+
+        Checking the error of a division by performing it at higher precision::
+
+            >>> fdiv(2, 3) - fdiv(2, 3, prec=100)
+            mpf('-3.7007434154172148e-17')
+
+        Unlike :func:`~mpmath.fadd`, :func:`~mpmath.fmul`, etc., exact division is not
+        allowed since the quotient of two floating-point numbers generally
+        does not have an exact floating-point representation. (In the
+        future this might be changed to allow the case where the division
+        is actually exact.)
+
+            >>> fdiv(2, 3, exact=True)
+            Traceback (most recent call last):
+              ...
+            ValueError: division is not an exact operation
+
+        """
+        prec, rounding = ctx._parse_prec(kwargs)
+        if not prec:
+            raise ValueError("division is not an exact operation")
+        x = ctx.convert(x)
+        y = ctx.convert(y)
+        if hasattr(x, '_mpf_'):
+            if hasattr(y, '_mpf_'):
+                return ctx.make_mpf(mpf_div(x._mpf_, y._mpf_, prec, rounding))
+            if hasattr(y, '_mpc_'):
+                return ctx.make_mpc(mpc_div((x._mpf_, fzero), y._mpc_, prec, rounding))
+        if hasattr(x, '_mpc_'):
+            if hasattr(y, '_mpf_'):
+                return ctx.make_mpc(mpc_div_mpf(x._mpc_, y._mpf_, prec, rounding))
+            if hasattr(y, '_mpc_'):
+                return ctx.make_mpc(mpc_div(x._mpc_, y._mpc_, prec, rounding))
+        raise ValueError("Arguments need to be mpf or mpc compatible numbers")
+
+    def nint_distance(ctx, x):
+        r"""
+        Return `(n,d)` where `n` is the nearest integer to `x` and `d` is
+        an estimate of `\log_2(|x-n|)`. If `d < 0`, `-d` gives the precision
+        (measured in bits) lost to cancellation when computing `x-n`.
+
+            >>> from mpmath import *
+            >>> n, d = nint_distance(5)
+            >>> print(n); print(d)
+            5
+            -inf
+            >>> n, d = nint_distance(mpf(5))
+            >>> print(n); print(d)
+            5
+            -inf
+            >>> n, d = nint_distance(mpf(5.00000001))
+            >>> print(n); print(d)
+            5
+            -26
+            >>> n, d = nint_distance(mpf(4.99999999))
+            >>> print(n); print(d)
+            5
+            -26
+            >>> n, d = nint_distance(mpc(5,10))
+            >>> print(n); print(d)
+            5
+            4
+            >>> n, d = nint_distance(mpc(5,0.000001))
+            >>> print(n); print(d)
+            5
+            -19
+
+        """
+        typx = type(x)
+        if typx in int_types:
+            return int(x), ctx.ninf
+        elif typx is rational.mpq:
+            p, q = x._mpq_
+            n, r = divmod(p, q)
+            if 2*r >= q:
+                n += 1
+            elif not r:
+                return n, ctx.ninf
+            # log(p/q-n) = log((p-nq)/q) = log(p-nq) - log(q)
+            d = bitcount(abs(p-n*q)) - bitcount(q)
+            return n, d
+        if hasattr(x, "_mpf_"):
+            re = x._mpf_
+            im_dist = ctx.ninf
+        elif hasattr(x, "_mpc_"):
+            re, im = x._mpc_
+            isign, iman, iexp, ibc = im
+            if iman:
+                im_dist = iexp + ibc
+            elif im == fzero:
+                im_dist = ctx.ninf
+            else:
+                raise ValueError("requires a finite number")
+        else:
+            x = ctx.convert(x)
+            if hasattr(x, "_mpf_") or hasattr(x, "_mpc_"):
+                return ctx.nint_distance(x)
+            else:
+                raise TypeError("requires an mpf/mpc")
+        sign, man, exp, bc = re
+        mag = exp+bc
+        # |x| < 0.5
+        if mag < 0:
+            n = 0
+            re_dist = mag
+        elif man:
+            # exact integer
+            if exp >= 0:
+                n = man << exp
+                re_dist = ctx.ninf
+            # exact half-integer
+            elif exp == -1:
+                n = (man>>1)+1
+                re_dist = 0
+            else:
+                d = (-exp-1)
+                t = man >> d
+                if t & 1:
+                    t += 1
+                    man = (t<<d) - man
+                else:
+                    man -= (t<<d)
+                n = t>>1   # int(t)>>1
+                re_dist = exp+bitcount(man)
+            if sign:
+                n = -n
+        elif re == fzero:
+            re_dist = ctx.ninf
+            n = 0
+        else:
+            raise ValueError("requires a finite number")
+        return n, max(re_dist, im_dist)
+
+    def fprod(ctx, factors):
+        r"""
+        Calculates a product containing a finite number of factors (for
+        infinite products, see :func:`~mpmath.nprod`). The factors will be
+        converted to mpmath numbers.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fprod([1, 2, 0.5, 7])
+            mpf('7.0')
+
+        """
+        orig = ctx.prec
+        try:
+            v = ctx.one
+            for p in factors:
+                v *= p
+        finally:
+            ctx.prec = orig
+        return +v
+
+    def rand(ctx):
+        """
+        Returns an ``mpf`` with value chosen randomly from `[0, 1)`.
+        The number of randomly generated bits in the mantissa is equal
+        to the working precision.
+        """
+        return ctx.make_mpf(mpf_rand(ctx._prec))
+
+    def fraction(ctx, p, q):
+        """
+        Given Python integers `(p, q)`, returns a lazy ``mpf`` representing
+        the fraction `p/q`. The value is updated with the precision.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15
+            >>> a = fraction(1,100)
+            >>> b = mpf(1)/100
+            >>> print(a); print(b)
+            0.01
+            0.01
+            >>> mp.dps = 30
+            >>> print(a); print(b)      # a will be accurate
+            0.01
+            0.0100000000000000002081668171172
+            >>> mp.dps = 15
+        """
+        return ctx.constant(lambda prec, rnd: from_rational(p, q, prec, rnd),
+            '%s/%s' % (p, q))
+
+    def absmin(ctx, x):
+        return abs(ctx.convert(x))
+
+    def absmax(ctx, x):
+        return abs(ctx.convert(x))
+
+    def _as_points(ctx, x):
+        # XXX: remove this?
+        if hasattr(x, '_mpi_'):
+            a, b = x._mpi_
+            return [ctx.make_mpf(a), ctx.make_mpf(b)]
+        return x
+
+    '''
+    def _zetasum(ctx, s, a, b):
+        """
+        Computes sum of k^(-s) for k = a, a+1, ..., b with a, b both small
+        integers.
+        """
+        a = int(a)
+        b = int(b)
+        s = ctx.convert(s)
+        prec, rounding = ctx._prec_rounding
+        if hasattr(s, '_mpf_'):
+            v = ctx.make_mpf(libmp.mpf_zetasum(s._mpf_, a, b, prec))
+        elif hasattr(s, '_mpc_'):
+            v = ctx.make_mpc(libmp.mpc_zetasum(s._mpc_, a, b, prec))
+        return v
+    '''
+
+    def _zetasum_fast(ctx, s, a, n, derivatives=[0], reflect=False):
+        if not (ctx.isint(a) and hasattr(s, "_mpc_")):
+            raise NotImplementedError
+        a = int(a)
+        prec = ctx._prec
+        xs, ys = libmp.mpc_zetasum(s._mpc_, a, n, derivatives, reflect, prec)
+        xs = [ctx.make_mpc(x) for x in xs]
+        ys = [ctx.make_mpc(y) for y in ys]
+        return xs, ys
+
+class PrecisionManager:
+    def __init__(self, ctx, precfun, dpsfun, normalize_output=False):
+        self.ctx = ctx
+        self.precfun = precfun
+        self.dpsfun = dpsfun
+        self.normalize_output = normalize_output
+    def __call__(self, f):
+        @functools.wraps(f)
+        def g(*args, **kwargs):
+            orig = self.ctx.prec
+            try:
+                if self.precfun:
+                    self.ctx.prec = self.precfun(self.ctx.prec)
+                else:
+                    self.ctx.dps = self.dpsfun(self.ctx.dps)
+                if self.normalize_output:
+                    v = f(*args, **kwargs)
+                    if type(v) is tuple:
+                        return tuple([+a for a in v])
+                    return +v
+                else:
+                    return f(*args, **kwargs)
+            finally:
+                self.ctx.prec = orig
+        return g
+    def __enter__(self):
+        self.origp = self.ctx.prec
+        if self.precfun:
+            self.ctx.prec = self.precfun(self.ctx.prec)
+        else:
+            self.ctx.dps = self.dpsfun(self.ctx.dps)
+    def __exit__(self, exc_type, exc_val, exc_tb):
+        self.ctx.prec = self.origp
+        return False
+
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()

venv/lib/python3.10/site-packages/mpmath/ctx_mp_python.py

@@ -0,0 +1,1149 @@
+#from ctx_base import StandardBaseContext
+
+from .libmp.backend import basestring, exec_
+
+from .libmp import (MPZ, MPZ_ZERO, MPZ_ONE, int_types, repr_dps,
+    round_floor, round_ceiling, dps_to_prec, round_nearest, prec_to_dps,
+    ComplexResult, to_pickable, from_pickable, normalize,
+    from_int, from_float, from_npfloat, from_Decimal, from_str, to_int, to_float, to_str,
+    from_rational, from_man_exp,
+    fone, fzero, finf, fninf, fnan,
+    mpf_abs, mpf_pos, mpf_neg, mpf_add, mpf_sub, mpf_mul, mpf_mul_int,
+    mpf_div, mpf_rdiv_int, mpf_pow_int, mpf_mod,
+    mpf_eq, mpf_cmp, mpf_lt, mpf_gt, mpf_le, mpf_ge,
+    mpf_hash, mpf_rand,
+    mpf_sum,
+    bitcount, to_fixed,
+    mpc_to_str,
+    mpc_to_complex, mpc_hash, mpc_pos, mpc_is_nonzero, mpc_neg, mpc_conjugate,
+    mpc_abs, mpc_add, mpc_add_mpf, mpc_sub, mpc_sub_mpf, mpc_mul, mpc_mul_mpf,
+    mpc_mul_int, mpc_div, mpc_div_mpf, mpc_pow, mpc_pow_mpf, mpc_pow_int,
+    mpc_mpf_div,
+    mpf_pow,
+    mpf_pi, mpf_degree, mpf_e, mpf_phi, mpf_ln2, mpf_ln10,
+    mpf_euler, mpf_catalan, mpf_apery, mpf_khinchin,
+    mpf_glaisher, mpf_twinprime, mpf_mertens,
+    int_types)
+
+from . import rational
+from . import function_docs
+
+new = object.__new__
+
+class mpnumeric(object):
+    """Base class for mpf and mpc."""
+    __slots__ = []
+    def __new__(cls, val):
+        raise NotImplementedError
+
+class _mpf(mpnumeric):
+    """
+    An mpf instance holds a real-valued floating-point number. mpf:s
+    work analogously to Python floats, but support arbitrary-precision
+    arithmetic.
+    """
+    __slots__ = ['_mpf_']
+
+    def __new__(cls, val=fzero, **kwargs):
+        """A new mpf can be created from a Python float, an int, a
+        or a decimal string representing a number in floating-point
+        format."""
+        prec, rounding = cls.context._prec_rounding
+        if kwargs:
+            prec = kwargs.get('prec', prec)
+            if 'dps' in kwargs:
+                prec = dps_to_prec(kwargs['dps'])
+            rounding = kwargs.get('rounding', rounding)
+        if type(val) is cls:
+            sign, man, exp, bc = val._mpf_
+            if (not man) and exp:
+                return val
+            v = new(cls)
+            v._mpf_ = normalize(sign, man, exp, bc, prec, rounding)
+            return v
+        elif type(val) is tuple:
+            if len(val) == 2:
+                v = new(cls)
+                v._mpf_ = from_man_exp(val[0], val[1], prec, rounding)
+                return v
+            if len(val) == 4:
+                if val not in (finf, fninf, fnan):
+                    sign, man, exp, bc = val
+                    val = normalize(sign, MPZ(man), exp, bc, prec, rounding)
+                v = new(cls)
+                v._mpf_ = val
+                return v
+            raise ValueError
+        else:
+            v = new(cls)
+            v._mpf_ = mpf_pos(cls.mpf_convert_arg(val, prec, rounding), prec, rounding)
+            return v
+
+    @classmethod
+    def mpf_convert_arg(cls, x, prec, rounding):
+        if isinstance(x, int_types): return from_int(x)
+        if isinstance(x, float): return from_float(x)
+        if isinstance(x, basestring): return from_str(x, prec, rounding)
+        if isinstance(x, cls.context.constant): return x.func(prec, rounding)
+        if hasattr(x, '_mpf_'): return x._mpf_
+        if hasattr(x, '_mpmath_'):
+            t = cls.context.convert(x._mpmath_(prec, rounding))
+            if hasattr(t, '_mpf_'):
+                return t._mpf_
+        if hasattr(x, '_mpi_'):
+            a, b = x._mpi_
+            if a == b:
+                return a
+            raise ValueError("can only create mpf from zero-width interval")
+        raise TypeError("cannot create mpf from " + repr(x))
+
+    @classmethod
+    def mpf_convert_rhs(cls, x):
+        if isinstance(x, int_types): return from_int(x)
+        if isinstance(x, float): return from_float(x)
+        if isinstance(x, complex_types): return cls.context.mpc(x)
+        if isinstance(x, rational.mpq):
+            p, q = x._mpq_
+            return from_rational(p, q, cls.context.prec)
+        if hasattr(x, '_mpf_'): return x._mpf_
+        if hasattr(x, '_mpmath_'):
+            t = cls.context.convert(x._mpmath_(*cls.context._prec_rounding))
+            if hasattr(t, '_mpf_'):
+                return t._mpf_
+            return t
+        return NotImplemented
+
+    @classmethod
+    def mpf_convert_lhs(cls, x):
+        x = cls.mpf_convert_rhs(x)
+        if type(x) is tuple:
+            return cls.context.make_mpf(x)
+        return x
+
+    man_exp = property(lambda self: self._mpf_[1:3])
+    man = property(lambda self: self._mpf_[1])
+    exp = property(lambda self: self._mpf_[2])
+    bc = property(lambda self: self._mpf_[3])
+
+    real = property(lambda self: self)
+    imag = property(lambda self: self.context.zero)
+
+    conjugate = lambda self: self
+
+    def __getstate__(self): return to_pickable(self._mpf_)
+    def __setstate__(self, val): self._mpf_ = from_pickable(val)
+
+    def __repr__(s):
+        if s.context.pretty:
+            return str(s)
+        return "mpf('%s')" % to_str(s._mpf_, s.context._repr_digits)
+
+    def __str__(s): return to_str(s._mpf_, s.context._str_digits)
+    def __hash__(s): return mpf_hash(s._mpf_)
+    def __int__(s): return int(to_int(s._mpf_))
+    def __long__(s): return long(to_int(s._mpf_))
+    def __float__(s): return to_float(s._mpf_, rnd=s.context._prec_rounding[1])
+    def __complex__(s): return complex(float(s))
+    def __nonzero__(s): return s._mpf_ != fzero
+
+    __bool__ = __nonzero__
+
+    def __abs__(s):
+        cls, new, (prec, rounding) = s._ctxdata
+        v = new(cls)
+        v._mpf_ = mpf_abs(s._mpf_, prec, rounding)
+        return v
+
+    def __pos__(s):
+        cls, new, (prec, rounding) = s._ctxdata
+        v = new(cls)
+        v._mpf_ = mpf_pos(s._mpf_, prec, rounding)
+        return v
+
+    def __neg__(s):
+        cls, new, (prec, rounding) = s._ctxdata
+        v = new(cls)
+        v._mpf_ = mpf_neg(s._mpf_, prec, rounding)
+        return v
+
+    def _cmp(s, t, func):
+        if hasattr(t, '_mpf_'):
+            t = t._mpf_
+        else:
+            t = s.mpf_convert_rhs(t)
+            if t is NotImplemented:
+                return t
+        return func(s._mpf_, t)
+
+    def __cmp__(s, t): return s._cmp(t, mpf_cmp)
+    def __lt__(s, t): return s._cmp(t, mpf_lt)
+    def __gt__(s, t): return s._cmp(t, mpf_gt)
+    def __le__(s, t): return s._cmp(t, mpf_le)
+    def __ge__(s, t): return s._cmp(t, mpf_ge)
+
+    def __ne__(s, t):
+        v = s.__eq__(t)
+        if v is NotImplemented:
+            return v
+        return not v
+
+    def __rsub__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if type(t) in int_types:
+            v = new(cls)
+            v._mpf_ = mpf_sub(from_int(t), s._mpf_, prec, rounding)
+            return v
+        t = s.mpf_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t - s
+
+    def __rdiv__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if isinstance(t, int_types):
+            v = new(cls)
+            v._mpf_ = mpf_rdiv_int(t, s._mpf_, prec, rounding)
+            return v
+        t = s.mpf_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t / s
+
+    def __rpow__(s, t):
+        t = s.mpf_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t ** s
+
+    def __rmod__(s, t):
+        t = s.mpf_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t % s
+
+    def sqrt(s):
+        return s.context.sqrt(s)
+
+    def ae(s, t, rel_eps=None, abs_eps=None):
+        return s.context.almosteq(s, t, rel_eps, abs_eps)
+
+    def to_fixed(self, prec):
+        return to_fixed(self._mpf_, prec)
+
+    def __round__(self, *args):
+        return round(float(self), *args)
+
+mpf_binary_op = """
+def %NAME%(self, other):
+    mpf, new, (prec, rounding) = self._ctxdata
+    sval = self._mpf_
+    if hasattr(other, '_mpf_'):
+        tval = other._mpf_
+        %WITH_MPF%
+    ttype = type(other)
+    if ttype in int_types:
+        %WITH_INT%
+    elif ttype is float:
+        tval = from_float(other)
+        %WITH_MPF%
+    elif hasattr(other, '_mpc_'):
+        tval = other._mpc_
+        mpc = type(other)
+        %WITH_MPC%
+    elif ttype is complex:
+        tval = from_float(other.real), from_float(other.imag)
+        mpc = self.context.mpc
+        %WITH_MPC%
+    if isinstance(other, mpnumeric):
+        return NotImplemented
+    try:
+        other = mpf.context.convert(other, strings=False)
+    except TypeError:
+        return NotImplemented
+    return self.%NAME%(other)
+"""
+
+return_mpf = "; obj = new(mpf); obj._mpf_ = val; return obj"
+return_mpc = "; obj = new(mpc); obj._mpc_ = val; return obj"
+
+mpf_pow_same = """
+        try:
+            val = mpf_pow(sval, tval, prec, rounding) %s
+        except ComplexResult:
+            if mpf.context.trap_complex:
+                raise
+            mpc = mpf.context.mpc
+            val = mpc_pow((sval, fzero), (tval, fzero), prec, rounding) %s
+""" % (return_mpf, return_mpc)
+
+def binary_op(name, with_mpf='', with_int='', with_mpc=''):
+    code = mpf_binary_op
+    code = code.replace("%WITH_INT%", with_int)
+    code = code.replace("%WITH_MPC%", with_mpc)
+    code = code.replace("%WITH_MPF%", with_mpf)
+    code = code.replace("%NAME%", name)
+    np = {}
+    exec_(code, globals(), np)
+    return np[name]
+
+_mpf.__eq__ = binary_op('__eq__',
+    'return mpf_eq(sval, tval)',
+    'return mpf_eq(sval, from_int(other))',
+    'return (tval[1] == fzero) and mpf_eq(tval[0], sval)')
+
+_mpf.__add__ = binary_op('__add__',
+    'val = mpf_add(sval, tval, prec, rounding)' + return_mpf,
+    'val = mpf_add(sval, from_int(other), prec, rounding)' + return_mpf,
+    'val = mpc_add_mpf(tval, sval, prec, rounding)' + return_mpc)
+
+_mpf.__sub__ = binary_op('__sub__',
+    'val = mpf_sub(sval, tval, prec, rounding)' + return_mpf,
+    'val = mpf_sub(sval, from_int(other), prec, rounding)' + return_mpf,
+    'val = mpc_sub((sval, fzero), tval, prec, rounding)' + return_mpc)
+
+_mpf.__mul__ = binary_op('__mul__',
+    'val = mpf_mul(sval, tval, prec, rounding)' + return_mpf,
+    'val = mpf_mul_int(sval, other, prec, rounding)' + return_mpf,
+    'val = mpc_mul_mpf(tval, sval, prec, rounding)' + return_mpc)
+
+_mpf.__div__ = binary_op('__div__',
+    'val = mpf_div(sval, tval, prec, rounding)' + return_mpf,
+    'val = mpf_div(sval, from_int(other), prec, rounding)' + return_mpf,
+    'val = mpc_mpf_div(sval, tval, prec, rounding)' + return_mpc)
+
+_mpf.__mod__ = binary_op('__mod__',
+    'val = mpf_mod(sval, tval, prec, rounding)' + return_mpf,
+    'val = mpf_mod(sval, from_int(other), prec, rounding)' + return_mpf,
+    'raise NotImplementedError("complex modulo")')
+
+_mpf.__pow__ = binary_op('__pow__',
+    mpf_pow_same,
+    'val = mpf_pow_int(sval, other, prec, rounding)' + return_mpf,
+    'val = mpc_pow((sval, fzero), tval, prec, rounding)' + return_mpc)
+
+_mpf.__radd__ = _mpf.__add__
+_mpf.__rmul__ = _mpf.__mul__
+_mpf.__truediv__ = _mpf.__div__
+_mpf.__rtruediv__ = _mpf.__rdiv__
+
+
+class _constant(_mpf):
+    """Represents a mathematical constant with dynamic precision.
+    When printed or used in an arithmetic operation, a constant
+    is converted to a regular mpf at the working precision. A
+    regular mpf can also be obtained using the operation +x."""
+
+    def __new__(cls, func, name, docname=''):
+        a = object.__new__(cls)
+        a.name = name
+        a.func = func
+        a.__doc__ = getattr(function_docs, docname, '')
+        return a
+
+    def __call__(self, prec=None, dps=None, rounding=None):
+        prec2, rounding2 = self.context._prec_rounding
+        if not prec: prec = prec2
+        if not rounding: rounding = rounding2
+        if dps: prec = dps_to_prec(dps)
+        return self.context.make_mpf(self.func(prec, rounding))
+
+    @property
+    def _mpf_(self):
+        prec, rounding = self.context._prec_rounding
+        return self.func(prec, rounding)
+
+    def __repr__(self):
+        return "<%s: %s~>" % (self.name, self.context.nstr(self(dps=15)))
+
+
+class _mpc(mpnumeric):
+    """
+    An mpc represents a complex number using a pair of mpf:s (one
+    for the real part and another for the imaginary part.) The mpc
+    class behaves fairly similarly to Python's complex type.
+    """
+
+    __slots__ = ['_mpc_']
+
+    def __new__(cls, real=0, imag=0):
+        s = object.__new__(cls)
+        if isinstance(real, complex_types):
+            real, imag = real.real, real.imag
+        elif hasattr(real, '_mpc_'):
+            s._mpc_ = real._mpc_
+            return s
+        real = cls.context.mpf(real)
+        imag = cls.context.mpf(imag)
+        s._mpc_ = (real._mpf_, imag._mpf_)
+        return s
+
+    real = property(lambda self: self.context.make_mpf(self._mpc_[0]))
+    imag = property(lambda self: self.context.make_mpf(self._mpc_[1]))
+
+    def __getstate__(self):
+        return to_pickable(self._mpc_[0]), to_pickable(self._mpc_[1])
+
+    def __setstate__(self, val):
+        self._mpc_ = from_pickable(val[0]), from_pickable(val[1])
+
+    def __repr__(s):
+        if s.context.pretty:
+            return str(s)
+        r = repr(s.real)[4:-1]
+        i = repr(s.imag)[4:-1]
+        return "%s(real=%s, imag=%s)" % (type(s).__name__, r, i)
+
+    def __str__(s):
+        return "(%s)" % mpc_to_str(s._mpc_, s.context._str_digits)
+
+    def __complex__(s):
+        return mpc_to_complex(s._mpc_, rnd=s.context._prec_rounding[1])
+
+    def __pos__(s):
+        cls, new, (prec, rounding) = s._ctxdata
+        v = new(cls)
+        v._mpc_ = mpc_pos(s._mpc_, prec, rounding)
+        return v
+
+    def __abs__(s):
+        prec, rounding = s.context._prec_rounding
+        v = new(s.context.mpf)
+        v._mpf_ = mpc_abs(s._mpc_, prec, rounding)
+        return v
+
+    def __neg__(s):
+        cls, new, (prec, rounding) = s._ctxdata
+        v = new(cls)
+        v._mpc_ = mpc_neg(s._mpc_, prec, rounding)
+        return v
+
+    def conjugate(s):
+        cls, new, (prec, rounding) = s._ctxdata
+        v = new(cls)
+        v._mpc_ = mpc_conjugate(s._mpc_, prec, rounding)
+        return v
+
+    def __nonzero__(s):
+        return mpc_is_nonzero(s._mpc_)
+
+    __bool__ = __nonzero__
+
+    def __hash__(s):
+        return mpc_hash(s._mpc_)
+
+    @classmethod
+    def mpc_convert_lhs(cls, x):
+        try:
+            y = cls.context.convert(x)
+            return y
+        except TypeError:
+            return NotImplemented
+
+    def __eq__(s, t):
+        if not hasattr(t, '_mpc_'):
+            if isinstance(t, str):
+                return False
+            t = s.mpc_convert_lhs(t)
+            if t is NotImplemented:
+                return t
+        return s.real == t.real and s.imag == t.imag
+
+    def __ne__(s, t):
+        b = s.__eq__(t)
+        if b is NotImplemented:
+            return b
+        return not b
+
+    def _compare(*args):
+        raise TypeError("no ordering relation is defined for complex numbers")
+
+    __gt__ = _compare
+    __le__ = _compare
+    __gt__ = _compare
+    __ge__ = _compare
+
+    def __add__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if not hasattr(t, '_mpc_'):
+            t = s.mpc_convert_lhs(t)
+            if t is NotImplemented:
+                return t
+            if hasattr(t, '_mpf_'):
+                v = new(cls)
+                v._mpc_ = mpc_add_mpf(s._mpc_, t._mpf_, prec, rounding)
+                return v
+        v = new(cls)
+        v._mpc_ = mpc_add(s._mpc_, t._mpc_, prec, rounding)
+        return v
+
+    def __sub__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if not hasattr(t, '_mpc_'):
+            t = s.mpc_convert_lhs(t)
+            if t is NotImplemented:
+                return t
+            if hasattr(t, '_mpf_'):
+                v = new(cls)
+                v._mpc_ = mpc_sub_mpf(s._mpc_, t._mpf_, prec, rounding)
+                return v
+        v = new(cls)
+        v._mpc_ = mpc_sub(s._mpc_, t._mpc_, prec, rounding)
+        return v
+
+    def __mul__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if not hasattr(t, '_mpc_'):
+            if isinstance(t, int_types):
+                v = new(cls)
+                v._mpc_ = mpc_mul_int(s._mpc_, t, prec, rounding)
+                return v
+            t = s.mpc_convert_lhs(t)
+            if t is NotImplemented:
+                return t
+            if hasattr(t, '_mpf_'):
+                v = new(cls)
+                v._mpc_ = mpc_mul_mpf(s._mpc_, t._mpf_, prec, rounding)
+                return v
+            t = s.mpc_convert_lhs(t)
+        v = new(cls)
+        v._mpc_ = mpc_mul(s._mpc_, t._mpc_, prec, rounding)
+        return v
+
+    def __div__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if not hasattr(t, '_mpc_'):
+            t = s.mpc_convert_lhs(t)
+            if t is NotImplemented:
+                return t
+            if hasattr(t, '_mpf_'):
+                v = new(cls)
+                v._mpc_ = mpc_div_mpf(s._mpc_, t._mpf_, prec, rounding)
+                return v
+        v = new(cls)
+        v._mpc_ = mpc_div(s._mpc_, t._mpc_, prec, rounding)
+        return v
+
+    def __pow__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if isinstance(t, int_types):
+            v = new(cls)
+            v._mpc_ = mpc_pow_int(s._mpc_, t, prec, rounding)
+            return v
+        t = s.mpc_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        v = new(cls)
+        if hasattr(t, '_mpf_'):
+            v._mpc_ = mpc_pow_mpf(s._mpc_, t._mpf_, prec, rounding)
+        else:
+            v._mpc_ = mpc_pow(s._mpc_, t._mpc_, prec, rounding)
+        return v
+
+    __radd__ = __add__
+
+    def __rsub__(s, t):
+        t = s.mpc_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t - s
+
+    def __rmul__(s, t):
+        cls, new, (prec, rounding) = s._ctxdata
+        if isinstance(t, int_types):
+            v = new(cls)
+            v._mpc_ = mpc_mul_int(s._mpc_, t, prec, rounding)
+            return v
+        t = s.mpc_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t * s
+
+    def __rdiv__(s, t):
+        t = s.mpc_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t / s
+
+    def __rpow__(s, t):
+        t = s.mpc_convert_lhs(t)
+        if t is NotImplemented:
+            return t
+        return t ** s
+
+    __truediv__ = __div__
+    __rtruediv__ = __rdiv__
+
+    def ae(s, t, rel_eps=None, abs_eps=None):
+        return s.context.almosteq(s, t, rel_eps, abs_eps)
+
+
+complex_types = (complex, _mpc)
+
+
+class PythonMPContext(object):
+
+    def __init__(ctx):
+        ctx._prec_rounding = [53, round_nearest]
+        ctx.mpf = type('mpf', (_mpf,), {})
+        ctx.mpc = type('mpc', (_mpc,), {})
+        ctx.mpf._ctxdata = [ctx.mpf, new, ctx._prec_rounding]
+        ctx.mpc._ctxdata = [ctx.mpc, new, ctx._prec_rounding]
+        ctx.mpf.context = ctx
+        ctx.mpc.context = ctx
+        ctx.constant = type('constant', (_constant,), {})
+        ctx.constant._ctxdata = [ctx.mpf, new, ctx._prec_rounding]
+        ctx.constant.context = ctx
+
+    def make_mpf(ctx, v):
+        a = new(ctx.mpf)
+        a._mpf_ = v
+        return a
+
+    def make_mpc(ctx, v):
+        a = new(ctx.mpc)
+        a._mpc_ = v
+        return a
+
+    def default(ctx):
+        ctx._prec = ctx._prec_rounding[0] = 53
+        ctx._dps = 15
+        ctx.trap_complex = False
+
+    def _set_prec(ctx, n):
+        ctx._prec = ctx._prec_rounding[0] = max(1, int(n))
+        ctx._dps = prec_to_dps(n)
+
+    def _set_dps(ctx, n):
+        ctx._prec = ctx._prec_rounding[0] = dps_to_prec(n)
+        ctx._dps = max(1, int(n))
+
+    prec = property(lambda ctx: ctx._prec, _set_prec)
+    dps = property(lambda ctx: ctx._dps, _set_dps)
+
+    def convert(ctx, x, strings=True):
+        """
+        Converts *x* to an ``mpf`` or ``mpc``. If *x* is of type ``mpf``,
+        ``mpc``, ``int``, ``float``, ``complex``, the conversion
+        will be performed losslessly.
+
+        If *x* is a string, the result will be rounded to the present
+        working precision. Strings representing fractions or complex
+        numbers are permitted.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> mpmathify(3.5)
+            mpf('3.5')
+            >>> mpmathify('2.1')
+            mpf('2.1000000000000001')
+            >>> mpmathify('3/4')
+            mpf('0.75')
+            >>> mpmathify('2+3j')
+            mpc(real='2.0', imag='3.0')
+
+        """
+        if type(x) in ctx.types: return x
+        if isinstance(x, int_types): return ctx.make_mpf(from_int(x))
+        if isinstance(x, float): return ctx.make_mpf(from_float(x))
+        if isinstance(x, complex):
+            return ctx.make_mpc((from_float(x.real), from_float(x.imag)))
+        if type(x).__module__ == 'numpy': return ctx.npconvert(x)
+        if isinstance(x, numbers.Rational): # e.g. Fraction
+            try: x = rational.mpq(int(x.numerator), int(x.denominator))
+            except: pass
+        prec, rounding = ctx._prec_rounding
+        if isinstance(x, rational.mpq):
+            p, q = x._mpq_
+            return ctx.make_mpf(from_rational(p, q, prec))
+        if strings and isinstance(x, basestring):
+            try:
+                _mpf_ = from_str(x, prec, rounding)
+                return ctx.make_mpf(_mpf_)
+            except ValueError:
+                pass
+        if hasattr(x, '_mpf_'): return ctx.make_mpf(x._mpf_)
+        if hasattr(x, '_mpc_'): return ctx.make_mpc(x._mpc_)
+        if hasattr(x, '_mpmath_'):
+            return ctx.convert(x._mpmath_(prec, rounding))
+        if type(x).__module__ == 'decimal':
+            try: return ctx.make_mpf(from_Decimal(x, prec, rounding))
+            except: pass
+        return ctx._convert_fallback(x, strings)
+
+    def npconvert(ctx, x):
+        """
+        Converts *x* to an ``mpf`` or ``mpc``. *x* should be a numpy
+        scalar.
+        """
+        import numpy as np
+        if isinstance(x, np.integer): return ctx.make_mpf(from_int(int(x)))
+        if isinstance(x, np.floating): return ctx.make_mpf(from_npfloat(x))
+        if isinstance(x, np.complexfloating):
+            return ctx.make_mpc((from_npfloat(x.real), from_npfloat(x.imag)))
+        raise TypeError("cannot create mpf from " + repr(x))
+
+    def isnan(ctx, x):
+        """
+        Return *True* if *x* is a NaN (not-a-number), or for a complex
+        number, whether either the real or complex part is NaN;
+        otherwise return *False*::
+
+            >>> from mpmath import *
+            >>> isnan(3.14)
+            False
+            >>> isnan(nan)
+            True
+            >>> isnan(mpc(3.14,2.72))
+            False
+            >>> isnan(mpc(3.14,nan))
+            True
+
+        """
+        if hasattr(x, "_mpf_"):
+            return x._mpf_ == fnan
+        if hasattr(x, "_mpc_"):
+            return fnan in x._mpc_
+        if isinstance(x, int_types) or isinstance(x, rational.mpq):
+            return False
+        x = ctx.convert(x)
+        if hasattr(x, '_mpf_') or hasattr(x, '_mpc_'):
+            return ctx.isnan(x)
+        raise TypeError("isnan() needs a number as input")
+
+    def isinf(ctx, x):
+        """
+        Return *True* if the absolute value of *x* is infinite;
+        otherwise return *False*::
+
+            >>> from mpmath import *
+            >>> isinf(inf)
+            True
+            >>> isinf(-inf)
+            True
+            >>> isinf(3)
+            False
+            >>> isinf(3+4j)
+            False
+            >>> isinf(mpc(3,inf))
+            True
+            >>> isinf(mpc(inf,3))
+            True
+
+        """
+        if hasattr(x, "_mpf_"):
+            return x._mpf_ in (finf, fninf)
+        if hasattr(x, "_mpc_"):
+            re, im = x._mpc_
+            return re in (finf, fninf) or im in (finf, fninf)
+        if isinstance(x, int_types) or isinstance(x, rational.mpq):
+            return False
+        x = ctx.convert(x)
+        if hasattr(x, '_mpf_') or hasattr(x, '_mpc_'):
+            return ctx.isinf(x)
+        raise TypeError("isinf() needs a number as input")
+
+    def isnormal(ctx, x):
+        """
+        Determine whether *x* is "normal" in the sense of floating-point
+        representation; that is, return *False* if *x* is zero, an
+        infinity or NaN; otherwise return *True*. By extension, a
+        complex number *x* is considered "normal" if its magnitude is
+        normal::
+
+            >>> from mpmath import *
+            >>> isnormal(3)
+            True
+            >>> isnormal(0)
+            False
+            >>> isnormal(inf); isnormal(-inf); isnormal(nan)
+            False
+            False
+            False
+            >>> isnormal(0+0j)
+            False
+            >>> isnormal(0+3j)
+            True
+            >>> isnormal(mpc(2,nan))
+            False
+        """
+        if hasattr(x, "_mpf_"):
+            return bool(x._mpf_[1])
+        if hasattr(x, "_mpc_"):
+            re, im = x._mpc_
+            re_normal = bool(re[1])
+            im_normal = bool(im[1])
+            if re == fzero: return im_normal
+            if im == fzero: return re_normal
+            return re_normal and im_normal
+        if isinstance(x, int_types) or isinstance(x, rational.mpq):
+            return bool(x)
+        x = ctx.convert(x)
+        if hasattr(x, '_mpf_') or hasattr(x, '_mpc_'):
+            return ctx.isnormal(x)
+        raise TypeError("isnormal() needs a number as input")
+
+    def isint(ctx, x, gaussian=False):
+        """
+        Return *True* if *x* is integer-valued; otherwise return
+        *False*::
+
+            >>> from mpmath import *
+            >>> isint(3)
+            True
+            >>> isint(mpf(3))
+            True
+            >>> isint(3.2)
+            False
+            >>> isint(inf)
+            False
+
+        Optionally, Gaussian integers can be checked for::
+
+            >>> isint(3+0j)
+            True
+            >>> isint(3+2j)
+            False
+            >>> isint(3+2j, gaussian=True)
+            True
+
+        """
+        if isinstance(x, int_types):
+            return True
+        if hasattr(x, "_mpf_"):
+            sign, man, exp, bc = xval = x._mpf_
+            return bool((man and exp >= 0) or xval == fzero)
+        if hasattr(x, "_mpc_"):
+            re, im = x._mpc_
+            rsign, rman, rexp, rbc = re
+            isign, iman, iexp, ibc = im
+            re_isint = (rman and rexp >= 0) or re == fzero
+            if gaussian:
+                im_isint = (iman and iexp >= 0) or im == fzero
+                return re_isint and im_isint
+            return re_isint and im == fzero
+        if isinstance(x, rational.mpq):
+            p, q = x._mpq_
+            return p % q == 0
+        x = ctx.convert(x)
+        if hasattr(x, '_mpf_') or hasattr(x, '_mpc_'):
+            return ctx.isint(x, gaussian)
+        raise TypeError("isint() needs a number as input")
+
+    def fsum(ctx, terms, absolute=False, squared=False):
+        """
+        Calculates a sum containing a finite number of terms (for infinite
+        series, see :func:`~mpmath.nsum`). The terms will be converted to
+        mpmath numbers. For len(terms) > 2, this function is generally
+        faster and produces more accurate results than the builtin
+        Python function :func:`sum`.
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> fsum([1, 2, 0.5, 7])
+            mpf('10.5')
+
+        With squared=True each term is squared, and with absolute=True
+        the absolute value of each term is used.
+        """
+        prec, rnd = ctx._prec_rounding
+        real = []
+        imag = []
+        for term in terms:
+            reval = imval = 0
+            if hasattr(term, "_mpf_"):
+                reval = term._mpf_
+            elif hasattr(term, "_mpc_"):
+                reval, imval = term._mpc_
+            else:
+                term = ctx.convert(term)
+                if hasattr(term, "_mpf_"):
+                    reval = term._mpf_
+                elif hasattr(term, "_mpc_"):
+                    reval, imval = term._mpc_
+                else:
+                    raise NotImplementedError
+            if imval:
+                if squared:
+                    if absolute:
+                        real.append(mpf_mul(reval,reval))
+                        real.append(mpf_mul(imval,imval))
+                    else:
+                        reval, imval = mpc_pow_int((reval,imval),2,prec+10)
+                        real.append(reval)
+                        imag.append(imval)
+                elif absolute:
+                    real.append(mpc_abs((reval,imval), prec))
+                else:
+                    real.append(reval)
+                    imag.append(imval)
+            else:
+                if squared:
+                    reval = mpf_mul(reval, reval)
+                elif absolute:
+                    reval = mpf_abs(reval)
+                real.append(reval)
+        s = mpf_sum(real, prec, rnd, absolute)
+        if imag:
+            s = ctx.make_mpc((s, mpf_sum(imag, prec, rnd)))
+        else:
+            s = ctx.make_mpf(s)
+        return s
+
+    def fdot(ctx, A, B=None, conjugate=False):
+        r"""
+        Computes the dot product of the iterables `A` and `B`,
+
+        .. math ::
+
+            \sum_{k=0} A_k B_k.
+
+        Alternatively, :func:`~mpmath.fdot` accepts a single iterable of pairs.
+        In other words, ``fdot(A,B)`` and ``fdot(zip(A,B))`` are equivalent.
+        The elements are automatically converted to mpmath numbers.
+
+        With ``conjugate=True``, the elements in the second vector
+        will be conjugated:
+
+        .. math ::
+
+            \sum_{k=0} A_k \overline{B_k}
+
+        **Examples**
+
+            >>> from mpmath import *
+            >>> mp.dps = 15; mp.pretty = False
+            >>> A = [2, 1.5, 3]
+            >>> B = [1, -1, 2]
+            >>> fdot(A, B)
+            mpf('6.5')
+            >>> list(zip(A, B))
+            [(2, 1), (1.5, -1), (3, 2)]
+            >>> fdot(_)
+            mpf('6.5')
+            >>> A = [2, 1.5, 3j]
+            >>> B = [1+j, 3, -1-j]
+            >>> fdot(A, B)
+            mpc(real='9.5', imag='-1.0')
+            >>> fdot(A, B, conjugate=True)
+            mpc(real='3.5', imag='-5.0')
+
+        """
+        if B is not None:
+            A = zip(A, B)
+        prec, rnd = ctx._prec_rounding
+        real = []
+        imag = []
+        hasattr_ = hasattr
+        types = (ctx.mpf, ctx.mpc)
+        for a, b in A:
+            if type(a) not in types: a = ctx.convert(a)
+            if type(b) not in types: b = ctx.convert(b)
+            a_real = hasattr_(a, "_mpf_")
+            b_real = hasattr_(b, "_mpf_")
+            if a_real and b_real:
+                real.append(mpf_mul(a._mpf_, b._mpf_))
+                continue
+            a_complex = hasattr_(a, "_mpc_")
+            b_complex = hasattr_(b, "_mpc_")
+            if a_real and b_complex:
+                aval = a._mpf_
+                bre, bim = b._mpc_
+                if conjugate:
+                    bim = mpf_neg(bim)
+                real.append(mpf_mul(aval, bre))
+                imag.append(mpf_mul(aval, bim))
+            elif b_real and a_complex:
+                are, aim = a._mpc_
+                bval = b._mpf_
+                real.append(mpf_mul(are, bval))
+                imag.append(mpf_mul(aim, bval))
+            elif a_complex and b_complex:
+                #re, im = mpc_mul(a._mpc_, b._mpc_, prec+20)
+                are, aim = a._mpc_
+                bre, bim = b._mpc_
+                if conjugate:
+                    bim = mpf_neg(bim)
+                real.append(mpf_mul(are, bre))
+                real.append(mpf_neg(mpf_mul(aim, bim)))
+                imag.append(mpf_mul(are, bim))
+                imag.append(mpf_mul(aim, bre))
+            else:
+                raise NotImplementedError
+        s = mpf_sum(real, prec, rnd)
+        if imag:
+            s = ctx.make_mpc((s, mpf_sum(imag, prec, rnd)))
+        else:
+            s = ctx.make_mpf(s)
+        return s
+
+    def _wrap_libmp_function(ctx, mpf_f, mpc_f=None, mpi_f=None, doc="<no doc>"):
+        """
+        Given a low-level mpf_ function, and optionally similar functions
+        for mpc_ and mpi_, defines the function as a context method.
+
+        It is assumed that the return type is the same as that of
+        the input; the exception is that propagation from mpf to mpc is possible
+        by raising ComplexResult.
+
+        """
+        def f(x, **kwargs):
+            if type(x) not in ctx.types:
+                x = ctx.convert(x)
+            prec, rounding = ctx._prec_rounding
+            if kwargs:
+                prec = kwargs.get('prec', prec)
+                if 'dps' in kwargs:
+                    prec = dps_to_prec(kwargs['dps'])
+                rounding = kwargs.get('rounding', rounding)
+            if hasattr(x, '_mpf_'):
+                try:
+                    return ctx.make_mpf(mpf_f(x._mpf_, prec, rounding))
+                except ComplexResult:
+                    # Handle propagation to complex
+                    if ctx.trap_complex:
+                        raise
+                    return ctx.make_mpc(mpc_f((x._mpf_, fzero), prec, rounding))
+            elif hasattr(x, '_mpc_'):
+                return ctx.make_mpc(mpc_f(x._mpc_, prec, rounding))
+            raise NotImplementedError("%s of a %s" % (name, type(x)))
+        name = mpf_f.__name__[4:]
+        f.__doc__ = function_docs.__dict__.get(name, "Computes the %s of x" % doc)
+        return f
+
+    # Called by SpecialFunctions.__init__()
+    @classmethod
+    def _wrap_specfun(cls, name, f, wrap):
+        if wrap:
+            def f_wrapped(ctx, *args, **kwargs):
+                convert = ctx.convert
+                args = [convert(a) for a in args]
+                prec = ctx.prec
+                try:
+                    ctx.prec += 10
+                    retval = f(ctx, *args, **kwargs)
+                finally:
+                    ctx.prec = prec
+                return +retval
+        else:
+            f_wrapped = f
+        f_wrapped.__doc__ = function_docs.__dict__.get(name, f.__doc__)
+        setattr(cls, name, f_wrapped)
+
+    def _convert_param(ctx, x):
+        if hasattr(x, "_mpc_"):
+            v, im = x._mpc_
+            if im != fzero:
+                return x, 'C'
+        elif hasattr(x, "_mpf_"):
+            v = x._mpf_
+        else:
+            if type(x) in int_types:
+                return int(x), 'Z'
+            p = None
+            if isinstance(x, tuple):
+                p, q = x
+            elif hasattr(x, '_mpq_'):
+                p, q = x._mpq_
+            elif isinstance(x, basestring) and '/' in x:
+                p, q = x.split('/')
+                p = int(p)
+                q = int(q)
+            if p is not None:
+                if not p % q:
+                    return p // q, 'Z'
+                return ctx.mpq(p,q), 'Q'
+            x = ctx.convert(x)
+            if hasattr(x, "_mpc_"):
+                v, im = x._mpc_
+                if im != fzero:
+                    return x, 'C'
+            elif hasattr(x, "_mpf_"):
+                v = x._mpf_
+            else:
+                return x, 'U'
+        sign, man, exp, bc = v
+        if man:
+            if exp >= -4:
+                if sign:
+                    man = -man
+                if exp >= 0:
+                    return int(man) << exp, 'Z'
+                if exp >= -4:
+                    p, q = int(man), (1<<(-exp))
+                    return ctx.mpq(p,q), 'Q'
+            x = ctx.make_mpf(v)
+            return x, 'R'
+        elif not exp:
+            return 0, 'Z'
+        else:
+            return x, 'U'
+
+    def _mpf_mag(ctx, x):
+        sign, man, exp, bc = x
+        if man:
+            return exp+bc
+        if x == fzero:
+            return ctx.ninf
+        if x == finf or x == fninf:
+            return ctx.inf
+        return ctx.nan
+
+    def mag(ctx, x):
+        """
+        Quick logarithmic magnitude estimate of a number. Returns an
+        integer or infinity `m` such that `|x| <= 2^m`. It is not
+        guaranteed that `m` is an optimal bound, but it will never
+        be too large by more than 2 (and probably not more than 1).
+
+        **Examples**
+
+            >>> from mpmath import *
+            >>> mp.pretty = True
+            >>> mag(10), mag(10.0), mag(mpf(10)), int(ceil(log(10,2)))
+            (4, 4, 4, 4)
+            >>> mag(10j), mag(10+10j)
+            (4, 5)
+            >>> mag(0.01), int(ceil(log(0.01,2)))
+            (-6, -6)
+            >>> mag(0), mag(inf), mag(-inf), mag(nan)
+            (-inf, +inf, +inf, nan)
+
+        """
+        if hasattr(x, "_mpf_"):
+            return ctx._mpf_mag(x._mpf_)
+        elif hasattr(x, "_mpc_"):
+            r, i = x._mpc_
+            if r == fzero:
+                return ctx._mpf_mag(i)
+            if i == fzero:
+                return ctx._mpf_mag(r)
+            return 1+max(ctx._mpf_mag(r), ctx._mpf_mag(i))
+        elif isinstance(x, int_types):
+            if x:
+                return bitcount(abs(x))
+            return ctx.ninf
+        elif isinstance(x, rational.mpq):
+            p, q = x._mpq_
+            if p:
+                return 1 + bitcount(abs(p)) - bitcount(q)
+            return ctx.ninf
+        else:
+            x = ctx.convert(x)
+            if hasattr(x, "_mpf_") or hasattr(x, "_mpc_"):
+                return ctx.mag(x)
+            else:
+                raise TypeError("requires an mpf/mpc")
+
+
+# Register with "numbers" ABC
+#     We do not subclass, hence we do not use the @abstractmethod checks. While
+#     this is less invasive it may turn out that we do not actually support
+#     parts of the expected interfaces.  See
+#     http://docs.python.org/2/library/numbers.html for list of abstract
+#     methods.
+try:
+    import numbers
+    numbers.Complex.register(_mpc)
+    numbers.Real.register(_mpf)
+except ImportError:
+    pass

venv/lib/python3.10/site-packages/mpmath/identification.py

@@ -0,0 +1,844 @@
+"""
+Implements the PSLQ algorithm for integer relation detection,
+and derivative algorithms for constant recognition.
+"""
+
+from .libmp.backend import xrange
+from .libmp import int_types, sqrt_fixed
+
+# round to nearest integer (can be done more elegantly...)
+def round_fixed(x, prec):
+    return ((x + (1<<(prec-1))) >> prec) << prec
+
+class IdentificationMethods(object):
+    pass
+
+
+def pslq(ctx, x, tol=None, maxcoeff=1000, maxsteps=100, verbose=False):
+    r"""
+    Given a vector of real numbers `x = [x_0, x_1, ..., x_n]`, ``pslq(x)``
+    uses the PSLQ algorithm to find a list of integers
+    `[c_0, c_1, ..., c_n]` such that
+
+    .. math ::
+
+        |c_1 x_1 + c_2 x_2 + ... + c_n x_n| < \mathrm{tol}
+
+    and such that `\max |c_k| < \mathrm{maxcoeff}`. If no such vector
+    exists, :func:`~mpmath.pslq` returns ``None``. The tolerance defaults to
+    3/4 of the working precision.
+
+    **Examples**
+
+    Find rational approximations for `\pi`::
+
+        >>> from mpmath import *
+        >>> mp.dps = 15; mp.pretty = True
+        >>> pslq([-1, pi], tol=0.01)
+        [22, 7]
+        >>> pslq([-1, pi], tol=0.001)
+        [355, 113]
+        >>> mpf(22)/7; mpf(355)/113; +pi
+        3.14285714285714
+        3.14159292035398
+        3.14159265358979
+
+    Pi is not a rational number with denominator less than 1000::
+
+        >>> pslq([-1, pi])
+        >>>
+
+    To within the standard precision, it can however be approximated
+    by at least one rational number with denominator less than `10^{12}`::
+
+        >>> p, q = pslq([-1, pi], maxcoeff=10**12)
+        >>> print(p); print(q)
+        238410049439
+        75888275702
+        >>> mpf(p)/q
+        3.14159265358979
+
+    The PSLQ algorithm can be applied to long vectors. For example,
+    we can investigate the rational (in)dependence of integer square
+    roots::
+
+        >>> mp.dps = 30
+        >>> pslq([sqrt(n) for n in range(2, 5+1)])
+        >>>
+        >>> pslq([sqrt(n) for n in range(2, 6+1)])
+        >>>
+        >>> pslq([sqrt(n) for n in range(2, 8+1)])
+        [2, 0, 0, 0, 0, 0, -1]
+
+    **Machin formulas**
+
+    A famous formula for `\pi` is Machin's,
+
+    .. math ::
+
+        \frac{\pi}{4} = 4 \operatorname{acot} 5 - \operatorname{acot} 239
+
+    There are actually infinitely many formulas of this type. Two
+    others are
+
+    .. math ::
+
+        \frac{\pi}{4} = \operatorname{acot} 1
+
+        \frac{\pi}{4} = 12 \operatorname{acot} 49 + 32 \operatorname{acot} 57
+            + 5 \operatorname{acot} 239 + 12 \operatorname{acot} 110443
+
+    We can easily verify the formulas using the PSLQ algorithm::
+
+        >>> mp.dps = 30
+        >>> pslq([pi/4, acot(1)])
+        [1, -1]
+        >>> pslq([pi/4, acot(5), acot(239)])
+        [1, -4, 1]
+        >>> pslq([pi/4, acot(49), acot(57), acot(239), acot(110443)])
+        [1, -12, -32, 5, -12]
+
+    We could try to generate a custom Machin-like formula by running
+    the PSLQ algorithm with a few inverse cotangent values, for example
+    acot(2), acot(3) ... acot(10). Unfortunately, there is a linear
+    dependence among these values, resulting in only that dependence
+    being detected, with a zero coefficient for `\pi`::
+
+        >>> pslq([pi] + [acot(n) for n in range(2,11)])
+        [0, 1, -1, 0, 0, 0, -1, 0, 0, 0]
+
+    We get better luck by removing linearly dependent terms::
+
+        >>> pslq([pi] + [acot(n) for n in range(2,11) if n not in (3, 5)])
+        [1, -8, 0, 0, 4, 0, 0, 0]
+
+    In other words, we found the following formula::
+
+        >>> 8*acot(2) - 4*acot(7)
+        3.14159265358979323846264338328
+        >>> +pi
+        3.14159265358979323846264338328
+
+    **Algorithm**
+
+    This is a fairly direct translation to Python of the pseudocode given by
+    David Bailey, "The PSLQ Integer Relation Algorithm":
+    http://www.cecm.sfu.ca/organics/papers/bailey/paper/html/node3.html
+
+    The present implementation uses fixed-point instead of floating-point
+    arithmetic, since this is significantly (about 7x) faster.
+    """
+
+    n = len(x)
+    if n < 2:
+        raise ValueError("n cannot be less than 2")
+
+    # At too low precision, the algorithm becomes meaningless
+    prec = ctx.prec
+    if prec < 53:
+        raise ValueError("prec cannot be less than 53")
+
+    if verbose and prec // max(2,n) < 5:
+        print("Warning: precision for PSLQ may be too low")
+
+    target = int(prec * 0.75)
+
+    if tol is None:
+        tol = ctx.mpf(2)**(-target)
+    else:
+        tol = ctx.convert(tol)
+
+    extra = 60
+    prec += extra
+
+    if verbose:
+        print("PSLQ using prec %i and tol %s" % (prec, ctx.nstr(tol)))
+
+    tol = ctx.to_fixed(tol, prec)
+    assert tol
+
+    # Convert to fixed-point numbers. The dummy None is added so we can
+    # use 1-based indexing. (This just allows us to be consistent with
+    # Bailey's indexing. The algorithm is 100 lines long, so debugging
+    # a single wrong index can be painful.)
+    x = [None] + [ctx.to_fixed(ctx.mpf(xk), prec) for xk in x]
+
+    # Sanity check on magnitudes
+    minx = min(abs(xx) for xx in x[1:])
+    if not minx:
+        raise ValueError("PSLQ requires a vector of nonzero numbers")
+    if minx < tol//100:
+        if verbose:
+            print("STOPPING: (one number is too small)")
+        return None
+
+    g = sqrt_fixed((4<<prec)//3, prec)
+    A = {}
+    B = {}
+    H = {}
+    # Initialization
+    # step 1
+    for i in xrange(1, n+1):
+        for j in xrange(1, n+1):
+            A[i,j] = B[i,j] = (i==j) << prec
+            H[i,j] = 0
+    # step 2
+    s = [None] + [0] * n
+    for k in xrange(1, n+1):
+        t = 0
+        for j in xrange(k, n+1):
+            t += (x[j]**2 >> prec)
+        s[k] = sqrt_fixed(t, prec)
+    t = s[1]
+    y = x[:]
+    for k in xrange(1, n+1):
+        y[k] = (x[k] << prec) // t
+        s[k] = (s[k] << prec) // t
+    # step 3
+    for i in xrange(1, n+1):
+        for j in xrange(i+1, n):
+            H[i,j] = 0
+        if i <= n-1:
+            if s[i]:
+                H[i,i] = (s[i+1] << prec) // s[i]
+            else:
+                H[i,i] = 0
+        for j in range(1, i):
+            sjj1 = s[j]*s[j+1]
+            if sjj1:
+                H[i,j] = ((-y[i]*y[j])<<prec)//sjj1
+            else:
+                H[i,j] = 0
+    # step 4
+    for i in xrange(2, n+1):
+        for j in xrange(i-1, 0, -1):
+            #t = floor(H[i,j]/H[j,j] + 0.5)
+            if H[j,j]:
+                t = round_fixed((H[i,j] << prec)//H[j,j], prec)
+            else:
+                #t = 0
+                continue
+            y[j] = y[j] + (t*y[i] >> prec)
+            for k in xrange(1, j+1):
+                H[i,k] = H[i,k] - (t*H[j,k] >> prec)
+            for k in xrange(1, n+1):
+                A[i,k] = A[i,k] - (t*A[j,k] >> prec)
+                B[k,j] = B[k,j] + (t*B[k,i] >> prec)
+    # Main algorithm
+    for REP in range(maxsteps):
+        # Step 1
+        m = -1
+        szmax = -1
+        for i in range(1, n):
+            h = H[i,i]
+            sz = (g**i * abs(h)) >> (prec*(i-1))
+            if sz > szmax:
+                m = i
+                szmax = sz
+        # Step 2
+        y[m], y[m+1] = y[m+1], y[m]
+        for i in xrange(1,n+1): H[m,i], H[m+1,i] = H[m+1,i], H[m,i]
+        for i in xrange(1,n+1): A[m,i], A[m+1,i] = A[m+1,i], A[m,i]
+        for i in xrange(1,n+1): B[i,m], B[i,m+1] = B[i,m+1], B[i,m]
+        # Step 3
+        if m <= n - 2:
+            t0 = sqrt_fixed((H[m,m]**2 + H[m,m+1]**2)>>prec, prec)
+            # A zero element probably indicates that the precision has
+            # been exhausted. XXX: this could be spurious, due to
+            # using fixed-point arithmetic
+            if not t0:
+                break
+            t1 = (H[m,m] << prec) // t0
+            t2 = (H[m,m+1] << prec) // t0
+            for i in xrange(m, n+1):
+                t3 = H[i,m]
+                t4 = H[i,m+1]
+                H[i,m] = (t1*t3+t2*t4) >> prec
+                H[i,m+1] = (-t2*t3+t1*t4) >> prec
+        # Step 4
+        for i in xrange(m+1, n+1):
+            for j in xrange(min(i-1, m+1), 0, -1):
+                try:
+                    t = round_fixed((H[i,j] << prec)//H[j,j], prec)
+                # Precision probably exhausted
+                except ZeroDivisionError:
+                    break
+                y[j] = y[j] + ((t*y[i]) >> prec)
+                for k in xrange(1, j+1):
+                    H[i,k] = H[i,k] - (t*H[j,k] >> prec)
+                for k in xrange(1, n+1):
+                    A[i,k] = A[i,k] - (t*A[j,k] >> prec)
+                    B[k,j] = B[k,j] + (t*B[k,i] >> prec)
+        # Until a relation is found, the error typically decreases
+        # slowly (e.g. a factor 1-10) with each step TODO: we could
+        # compare err from two successive iterations. If there is a
+        # large drop (several orders of magnitude), that indicates a
+        # "high quality" relation was detected. Reporting this to
+        # the user somehow might be useful.
+        best_err = maxcoeff<<prec
+        for i in xrange(1, n+1):
+            err = abs(y[i])
+            # Maybe we are done?
+            if err < tol:
+                # We are done if the coefficients are acceptable
+                vec = [int(round_fixed(B[j,i], prec) >> prec) for j in \
+                range(1,n+1)]
+                if max(abs(v) for v in vec) < maxcoeff:
+                    if verbose:
+                        print("FOUND relation at iter %i/%i, error: %s" % \
+                            (REP, maxsteps, ctx.nstr(err / ctx.mpf(2)**prec, 1)))
+                    return vec
+            best_err = min(err, best_err)
+        # Calculate a lower bound for the norm. We could do this
+        # more exactly (using the Euclidean norm) but there is probably
+        # no practical benefit.
+        recnorm = max(abs(h) for h in H.values())
+        if recnorm:
+            norm = ((1 << (2*prec)) // recnorm) >> prec
+            norm //= 100
+        else:
+            norm = ctx.inf
+        if verbose:
+            print("%i/%i:  Error: %8s   Norm: %s" % \
+                (REP, maxsteps, ctx.nstr(best_err / ctx.mpf(2)**prec, 1), norm))
+        if norm >= maxcoeff:
+            break
+    if verbose:
+        print("CANCELLING after step %i/%i." % (REP, maxsteps))
+        print("Could not find an integer relation. Norm bound: %s" % norm)
+    return None
+
+def findpoly(ctx, x, n=1, **kwargs):
+    r"""
+    ``findpoly(x, n)`` returns the coefficients of an integer
+    polynomial `P` of degree at most `n` such that `P(x) \approx 0`.
+    If no polynomial having `x` as a root can be found,
+    :func:`~mpmath.findpoly` returns ``None``.
+
+    :func:`~mpmath.findpoly` works by successively calling :func:`~mpmath.pslq` with
+    the vectors `[1, x]`, `[1, x, x^2]`, `[1, x, x^2, x^3]`, ...,
+    `[1, x, x^2, .., x^n]` as input. Keyword arguments given to
+    :func:`~mpmath.findpoly` are forwarded verbatim to :func:`~mpmath.pslq`. In
+    particular, you can specify a tolerance for `P(x)` with ``tol``
+    and a maximum permitted coefficient size with ``maxcoeff``.
+
+    For large values of `n`, it is recommended to run :func:`~mpmath.findpoly`
+    at high precision; preferably 50 digits or more.
+
+    **Examples**
+
+    By default (degree `n = 1`), :func:`~mpmath.findpoly` simply finds a linear
+    polynomial with a rational root::
+
+        >>> from mpmath import *
+        >>> mp.dps = 15; mp.pretty = True
+        >>> findpoly(0.7)
+        [-10, 7]
+
+    The generated coefficient list is valid input to ``polyval`` and
+    ``polyroots``::
+
+        >>> nprint(polyval(findpoly(phi, 2), phi), 1)
+        -2.0e-16
+        >>> for r in polyroots(findpoly(phi, 2)):
+        ...     print(r)
+        ...
+        -0.618033988749895
+        1.61803398874989
+
+    Numbers of the form `m + n \sqrt p` for integers `(m, n, p)` are
+    solutions to quadratic equations. As we find here, `1+\sqrt 2`
+    is a root of the polynomial `x^2 - 2x - 1`::
+
+        >>> findpoly(1+sqrt(2), 2)
+        [1, -2, -1]
+        >>> findroot(lambda x: x**2 - 2*x - 1, 1)
+        2.4142135623731
+
+    Despite only containing square roots, the following number results
+    in a polynomial of degree 4::
+
+        >>> findpoly(sqrt(2)+sqrt(3), 4)
+        [1, 0, -10, 0, 1]
+
+    In fact, `x^4 - 10x^2 + 1` is the *minimal polynomial* of
+    `r = \sqrt 2 + \sqrt 3`, meaning that a rational polynomial of
+    lower degree having `r` as a root does not exist. Given sufficient
+    precision, :func:`~mpmath.findpoly` will usually find the correct
+    minimal polynomial of a given algebraic number.
+
+    **Non-algebraic numbers**
+
+    If :func:`~mpmath.findpoly` fails to find a polynomial with given
+    coefficient size and tolerance constraints, that means no such
+    polynomial exists.
+
+    We can verify that `\pi` is not an algebraic number of degree 3 with
+    coefficients less than 1000::
+
+        >>> mp.dps = 15
+        >>> findpoly(pi, 3)
+        >>>
+
+    It is always possible to find an algebraic approximation of a number
+    using one (or several) of the following methods:
+
+        1. Increasing the permitted degree
+        2. Allowing larger coefficients
+        3. Reducing the tolerance
+
+    One example of each method is shown below::
+
+        >>> mp.dps = 15
+        >>> findpoly(pi, 4)
+        [95, -545, 863, -183, -298]
+        >>> findpoly(pi, 3, maxcoeff=10000)
+        [836, -1734, -2658, -457]
+        >>> findpoly(pi, 3, tol=1e-7)
+        [-4, 22, -29, -2]
+
+    It is unknown whether Euler's constant is transcendental (or even
+    irrational). We can use :func:`~mpmath.findpoly` to check that if is
+    an algebraic number, its minimal polynomial must have degree
+    at least 7 and a coefficient of magnitude at least 1000000::
+
+        >>> mp.dps = 200
+        >>> findpoly(euler, 6, maxcoeff=10**6, tol=1e-100, maxsteps=1000)
+        >>>
+
+    Note that the high precision and strict tolerance is necessary
+    for such high-degree runs, since otherwise unwanted low-accuracy
+    approximations will be detected. It may also be necessary to set
+    maxsteps high to prevent a premature exit (before the coefficient
+    bound has been reached). Running with ``verbose=True`` to get an
+    idea what is happening can be useful.
+    """
+    x = ctx.mpf(x)
+    if n < 1:
+        raise ValueError("n cannot be less than 1")
+    if x == 0:
+        return [1, 0]
+    xs = [ctx.mpf(1)]
+    for i in range(1,n+1):
+        xs.append(x**i)
+        a = ctx.pslq(xs, **kwargs)
+        if a is not None:
+            return a[::-1]
+
+def fracgcd(p, q):
+    x, y = p, q
+    while y:
+        x, y = y, x % y
+    if x != 1:
+        p //= x
+        q //= x
+    if q == 1:
+        return p
+    return p, q
+
+def pslqstring(r, constants):
+    q = r[0]
+    r = r[1:]
+    s = []
+    for i in range(len(r)):
+        p = r[i]
+        if p:
+            z = fracgcd(-p,q)
+            cs = constants[i][1]
+            if cs == '1':
+                cs = ''
+            else:
+                cs = '*' + cs
+            if isinstance(z, int_types):
+                if z > 0: term = str(z) + cs
+                else:     term = ("(%s)" % z) + cs
+            else:
+                term = ("(%s/%s)" % z) + cs
+            s.append(term)
+    s = ' + '.join(s)
+    if '+' in s or '*' in s:
+        s = '(' + s + ')'
+    return s or '0'
+
+def prodstring(r, constants):
+    q = r[0]
+    r = r[1:]
+    num = []
+    den = []
+    for i in range(len(r)):
+        p = r[i]
+        if p:
+            z = fracgcd(-p,q)
+            cs = constants[i][1]
+            if isinstance(z, int_types):
+                if abs(z) == 1: t = cs
+                else:           t = '%s**%s' % (cs, abs(z))
+                ([num,den][z<0]).append(t)
+            else:
+                t = '%s**(%s/%s)' % (cs, abs(z[0]), z[1])
+                ([num,den][z[0]<0]).append(t)
+    num = '*'.join(num)
+    den = '*'.join(den)
+    if num and den: return "(%s)/(%s)" % (num, den)
+    if num: return num
+    if den: return "1/(%s)" % den
+
+def quadraticstring(ctx,t,a,b,c):
+    if c < 0:
+        a,b,c = -a,-b,-c
+    u1 = (-b+ctx.sqrt(b**2-4*a*c))/(2*c)
+    u2 = (-b-ctx.sqrt(b**2-4*a*c))/(2*c)
+    if abs(u1-t) < abs(u2-t):
+        if b:  s = '((%s+sqrt(%s))/%s)' % (-b,b**2-4*a*c,2*c)
+        else:  s = '(sqrt(%s)/%s)' % (-4*a*c,2*c)
+    else:
+        if b:  s = '((%s-sqrt(%s))/%s)' % (-b,b**2-4*a*c,2*c)
+        else:  s = '(-sqrt(%s)/%s)' % (-4*a*c,2*c)
+    return s
+
+# Transformation y = f(x,c), with inverse function x = f(y,c)
+# The third entry indicates whether the transformation is
+# redundant when c = 1
+transforms = [
+  (lambda ctx,x,c: x*c, '$y/$c', 0),
+  (lambda ctx,x,c: x/c, '$c*$y', 1),
+  (lambda ctx,x,c: c/x, '$c/$y', 0),
+  (lambda ctx,x,c: (x*c)**2, 'sqrt($y)/$c', 0),
+  (lambda ctx,x,c: (x/c)**2, '$c*sqrt($y)', 1),
+  (lambda ctx,x,c: (c/x)**2, '$c/sqrt($y)', 0),
+  (lambda ctx,x,c: c*x**2, 'sqrt($y)/sqrt($c)', 1),
+  (lambda ctx,x,c: x**2/c, 'sqrt($c)*sqrt($y)', 1),
+  (lambda ctx,x,c: c/x**2, 'sqrt($c)/sqrt($y)', 1),
+  (lambda ctx,x,c: ctx.sqrt(x*c), '$y**2/$c', 0),
+  (lambda ctx,x,c: ctx.sqrt(x/c), '$c*$y**2', 1),
+  (lambda ctx,x,c: ctx.sqrt(c/x), '$c/$y**2', 0),
+  (lambda ctx,x,c: c*ctx.sqrt(x), '$y**2/$c**2', 1),
+  (lambda ctx,x,c: ctx.sqrt(x)/c, '$c**2*$y**2', 1),
+  (lambda ctx,x,c: c/ctx.sqrt(x), '$c**2/$y**2', 1),
+  (lambda ctx,x,c: ctx.exp(x*c), 'log($y)/$c', 0),
+  (lambda ctx,x,c: ctx.exp(x/c), '$c*log($y)', 1),
+  (lambda ctx,x,c: ctx.exp(c/x), '$c/log($y)', 0),
+  (lambda ctx,x,c: c*ctx.exp(x), 'log($y/$c)', 1),
+  (lambda ctx,x,c: ctx.exp(x)/c, 'log($c*$y)', 1),
+  (lambda ctx,x,c: c/ctx.exp(x), 'log($c/$y)', 0),
+  (lambda ctx,x,c: ctx.ln(x*c), 'exp($y)/$c', 0),
+  (lambda ctx,x,c: ctx.ln(x/c), '$c*exp($y)', 1),
+  (lambda ctx,x,c: ctx.ln(c/x), '$c/exp($y)', 0),
+  (lambda ctx,x,c: c*ctx.ln(x), 'exp($y/$c)', 1),
+  (lambda ctx,x,c: ctx.ln(x)/c, 'exp($c*$y)', 1),
+  (lambda ctx,x,c: c/ctx.ln(x), 'exp($c/$y)', 0),
+]
+
+def identify(ctx, x, constants=[], tol=None, maxcoeff=1000, full=False,
+    verbose=False):
+    r"""
+    Given a real number `x`, ``identify(x)`` attempts to find an exact
+    formula for `x`. This formula is returned as a string. If no match
+    is found, ``None`` is returned. With ``full=True``, a list of
+    matching formulas is returned.
+
+    As a simple example, :func:`~mpmath.identify` will find an algebraic
+    formula for the golden ratio::
+
+        >>> from mpmath import *
+        >>> mp.dps = 15; mp.pretty = True
+        >>> identify(phi)
+        '((1+sqrt(5))/2)'
+
+    :func:`~mpmath.identify` can identify simple algebraic numbers and simple
+    combinations of given base constants, as well as certain basic
+    transformations thereof. More specifically, :func:`~mpmath.identify`
+    looks for the following:
+
+        1. Fractions
+        2. Quadratic algebraic numbers
+        3. Rational linear combinations of the base constants
+        4. Any of the above after first transforming `x` into `f(x)` where
+           `f(x)` is `1/x`, `\sqrt x`, `x^2`, `\log x` or `\exp x`, either
+           directly or with `x` or `f(x)` multiplied or divided by one of
+           the base constants
+        5. Products of fractional powers of the base constants and
+           small integers
+
+    Base constants can be given as a list of strings representing mpmath
+    expressions (:func:`~mpmath.identify` will ``eval`` the strings to numerical
+    values and use the original strings for the output), or as a dict of
+    formula:value pairs.
+
+    In order not to produce spurious results, :func:`~mpmath.identify` should
+    be used with high precision; preferably 50 digits or more.
+
+    **Examples**
+
+    Simple identifications can be performed safely at standard
+    precision. Here the default recognition of rational, algebraic,
+    and exp/log of algebraic numbers is demonstrated::
+
+        >>> mp.dps = 15
+        >>> identify(0.22222222222222222)
+        '(2/9)'
+        >>> identify(1.9662210973805663)
+        'sqrt(((24+sqrt(48))/8))'
+        >>> identify(4.1132503787829275)
+        'exp((sqrt(8)/2))'
+        >>> identify(0.881373587019543)
+        'log(((2+sqrt(8))/2))'
+
+    By default, :func:`~mpmath.identify` does not recognize `\pi`. At standard
+    precision it finds a not too useful approximation. At slightly
+    increased precision, this approximation is no longer accurate
+    enough and :func:`~mpmath.identify` more correctly returns ``None``::
+
+        >>> identify(pi)
+        '(2**(176/117)*3**(20/117)*5**(35/39))/(7**(92/117))'
+        >>> mp.dps = 30
+        >>> identify(pi)
+        >>>
+
+    Numbers such as `\pi`, and simple combinations of user-defined
+    constants, can be identified if they are provided explicitly::
+
+        >>> identify(3*pi-2*e, ['pi', 'e'])
+        '(3*pi + (-2)*e)'
+
+    Here is an example using a dict of constants. Note that the
+    constants need not be "atomic"; :func:`~mpmath.identify` can just
+    as well express the given number in terms of expressions
+    given by formulas::
+
+        >>> identify(pi+e, {'a':pi+2, 'b':2*e})
+        '((-2) + 1*a + (1/2)*b)'
+
+    Next, we attempt some identifications with a set of base constants.
+    It is necessary to increase the precision a bit.
+
+        >>> mp.dps = 50
+        >>> base = ['sqrt(2)','pi','log(2)']
+        >>> identify(0.25, base)
+        '(1/4)'
+        >>> identify(3*pi + 2*sqrt(2) + 5*log(2)/7, base)
+        '(2*sqrt(2) + 3*pi + (5/7)*log(2))'
+        >>> identify(exp(pi+2), base)
+        'exp((2 + 1*pi))'
+        >>> identify(1/(3+sqrt(2)), base)
+        '((3/7) + (-1/7)*sqrt(2))'
+        >>> identify(sqrt(2)/(3*pi+4), base)
+        'sqrt(2)/(4 + 3*pi)'
+        >>> identify(5**(mpf(1)/3)*pi*log(2)**2, base)
+        '5**(1/3)*pi*log(2)**2'
+
+    An example of an erroneous solution being found when too low
+    precision is used::
+
+        >>> mp.dps = 15
+        >>> identify(1/(3*pi-4*e+sqrt(8)), ['pi', 'e', 'sqrt(2)'])
+        '((11/25) + (-158/75)*pi + (76/75)*e + (44/15)*sqrt(2))'
+        >>> mp.dps = 50
+        >>> identify(1/(3*pi-4*e+sqrt(8)), ['pi', 'e', 'sqrt(2)'])
+        '1/(3*pi + (-4)*e + 2*sqrt(2))'
+
+    **Finding approximate solutions**
+
+    The tolerance ``tol`` defaults to 3/4 of the working precision.
+    Lowering the tolerance is useful for finding approximate matches.
+    We can for example try to generate approximations for pi::
+
+        >>> mp.dps = 15
+        >>> identify(pi, tol=1e-2)
+        '(22/7)'
+        >>> identify(pi, tol=1e-3)
+        '(355/113)'
+        >>> identify(pi, tol=1e-10)
+        '(5**(339/269))/(2**(64/269)*3**(13/269)*7**(92/269))'
+
+    With ``full=True``, and by supplying a few base constants,
+    ``identify`` can generate almost endless lists of approximations
+    for any number (the output below has been truncated to show only
+    the first few)::
+
+        >>> for p in identify(pi, ['e', 'catalan'], tol=1e-5, full=True):
+        ...     print(p)
+        ...  # doctest: +ELLIPSIS
+        e/log((6 + (-4/3)*e))
+        (3**3*5*e*catalan**2)/(2*7**2)
+        sqrt(((-13) + 1*e + 22*catalan))
+        log(((-6) + 24*e + 4*catalan)/e)
+        exp(catalan*((-1/5) + (8/15)*e))
+        catalan*(6 + (-6)*e + 15*catalan)
+        sqrt((5 + 26*e + (-3)*catalan))/e
+        e*sqrt(((-27) + 2*e + 25*catalan))
+        log(((-1) + (-11)*e + 59*catalan))
+        ((3/20) + (21/20)*e + (3/20)*catalan)
+        ...
+
+    The numerical values are roughly as close to `\pi` as permitted by the
+    specified tolerance:
+
+        >>> e/log(6-4*e/3)
+        3.14157719846001
+        >>> 135*e*catalan**2/98
+        3.14166950419369
+        >>> sqrt(e-13+22*catalan)
+        3.14158000062992
+        >>> log(24*e-6+4*catalan)-1
+        3.14158791577159
+
+    **Symbolic processing**
+
+    The output formula can be evaluated as a Python expression.
+    Note however that if fractions (like '2/3') are present in
+    the formula, Python's :func:`~mpmath.eval()` may erroneously perform
+    integer division. Note also that the output is not necessarily
+    in the algebraically simplest form::
+
+        >>> identify(sqrt(2))
+        '(sqrt(8)/2)'
+
+    As a solution to both problems, consider using SymPy's
+    :func:`~mpmath.sympify` to convert the formula into a symbolic expression.
+    SymPy can be used to pretty-print or further simplify the formula
+    symbolically::
+
+        >>> from sympy import sympify # doctest: +SKIP
+        >>> sympify(identify(sqrt(2))) # doctest: +SKIP
+        2**(1/2)
+
+    Sometimes :func:`~mpmath.identify` can simplify an expression further than
+    a symbolic algorithm::
+
+        >>> from sympy import simplify # doctest: +SKIP
+        >>> x = sympify('-1/(-3/2+(1/2)*5**(1/2))*(3/2-1/2*5**(1/2))**(1/2)') # doctest: +SKIP
+        >>> x # doctest: +SKIP
+        (3/2 - 5**(1/2)/2)**(-1/2)
+        >>> x = simplify(x) # doctest: +SKIP
+        >>> x # doctest: +SKIP
+        2/(6 - 2*5**(1/2))**(1/2)
+        >>> mp.dps = 30 # doctest: +SKIP
+        >>> x = sympify(identify(x.evalf(30))) # doctest: +SKIP
+        >>> x # doctest: +SKIP
+        1/2 + 5**(1/2)/2
+
+    (In fact, this functionality is available directly in SymPy as the
+    function :func:`~mpmath.nsimplify`, which is essentially a wrapper for
+    :func:`~mpmath.identify`.)
+
+    **Miscellaneous issues and limitations**
+
+    The input `x` must be a real number. All base constants must be
+    positive real numbers and must not be rationals or rational linear
+    combinations of each other.
+
+    The worst-case computation time grows quickly with the number of
+    base constants. Already with 3 or 4 base constants,
+    :func:`~mpmath.identify` may require several seconds to finish. To search
+    for relations among a large number of constants, you should
+    consider using :func:`~mpmath.pslq` directly.
+
+    The extended transformations are applied to x, not the constants
+    separately. As a result, ``identify`` will for example be able to
+    recognize ``exp(2*pi+3)`` with ``pi`` given as a base constant, but
+    not ``2*exp(pi)+3``. It will be able to recognize the latter if
+    ``exp(pi)`` is given explicitly as a base constant.
+
+    """
+
+    solutions = []
+
+    def addsolution(s):
+        if verbose: print("Found: ", s)
+        solutions.append(s)
+
+    x = ctx.mpf(x)
+
+    # Further along, x will be assumed positive
+    if x == 0:
+        if full: return ['0']
+        else:    return '0'
+    if x < 0:
+        sol = ctx.identify(-x, constants, tol, maxcoeff, full, verbose)
+        if sol is None:
+            return sol
+        if full:
+            return ["-(%s)"%s for s in sol]
+        else:
+            return "-(%s)" % sol
+
+    if tol:
+        tol = ctx.mpf(tol)
+    else:
+        tol = ctx.eps**0.7
+    M = maxcoeff
+
+    if constants:
+        if isinstance(constants, dict):
+            constants = [(ctx.mpf(v), name) for (name, v) in sorted(constants.items())]
+        else:
+            namespace = dict((name, getattr(ctx,name)) for name in dir(ctx))
+            constants = [(eval(p, namespace), p) for p in constants]
+    else:
+        constants = []
+
+    # We always want to find at least rational terms
+    if 1 not in [value for (name, value) in constants]:
+        constants = [(ctx.mpf(1), '1')] + constants
+
+    # PSLQ with simple algebraic and functional transformations
+    for ft, ftn, red in transforms:
+        for c, cn in constants:
+            if red and cn == '1':
+                continue
+            t = ft(ctx,x,c)
+            # Prevent exponential transforms from wreaking havoc
+            if abs(t) > M**2 or abs(t) < tol:
+                continue
+            # Linear combination of base constants
+            r = ctx.pslq([t] + [a[0] for a in constants], tol, M)
+            s = None
+            if r is not None and max(abs(uw) for uw in r) <= M and r[0]:
+                s = pslqstring(r, constants)
+            # Quadratic algebraic numbers
+            else:
+                q = ctx.pslq([ctx.one, t, t**2], tol, M)
+                if q is not None and len(q) == 3 and q[2]:
+                    aa, bb, cc = q
+                    if max(abs(aa),abs(bb),abs(cc)) <= M:
+                        s = quadraticstring(ctx,t,aa,bb,cc)
+            if s:
+                if cn == '1' and ('/$c' in ftn):
+                    s = ftn.replace('$y', s).replace('/$c', '')
+                else:
+                    s = ftn.replace('$y', s).replace('$c', cn)
+                addsolution(s)
+                if not full: return solutions[0]
+
+            if verbose:
+                print(".")
+
+    # Check for a direct multiplicative formula
+    if x != 1:
+        # Allow fractional powers of fractions
+        ilogs = [2,3,5,7]
+        # Watch out for existing fractional powers of fractions
+        logs = []
+        for a, s in constants:
+            if not sum(bool(ctx.findpoly(ctx.ln(a)/ctx.ln(i),1)) for i in ilogs):
+                logs.append((ctx.ln(a), s))
+        logs = [(ctx.ln(i),str(i)) for i in ilogs] + logs
+        r = ctx.pslq([ctx.ln(x)] + [a[0] for a in logs], tol, M)
+        if r is not None and max(abs(uw) for uw in r) <= M and r[0]:
+            addsolution(prodstring(r, logs))
+            if not full: return solutions[0]
+
+    if full:
+        return sorted(solutions, key=len)
+    else:
+        return None
+
+IdentificationMethods.pslq = pslq
+IdentificationMethods.findpoly = findpoly
+IdentificationMethods.identify = identify
+
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()

venv/lib/python3.10/site-packages/mpmath/math2.py

@@ -0,0 +1,672 @@
+"""
+This module complements the math and cmath builtin modules by providing
+fast machine precision versions of some additional functions (gamma, ...)
+and wrapping math/cmath functions so that they can be called with either
+real or complex arguments.
+"""
+
+import operator
+import math
+import cmath
+
+# Irrational (?) constants
+pi = 3.1415926535897932385
+e = 2.7182818284590452354
+sqrt2 = 1.4142135623730950488
+sqrt5 = 2.2360679774997896964
+phi = 1.6180339887498948482
+ln2 = 0.69314718055994530942
+ln10 = 2.302585092994045684
+euler = 0.57721566490153286061
+catalan = 0.91596559417721901505
+khinchin = 2.6854520010653064453
+apery = 1.2020569031595942854
+
+logpi = 1.1447298858494001741
+
+def _mathfun_real(f_real, f_complex):
+    def f(x, **kwargs):
+        if type(x) is float:
+            return f_real(x)
+        if type(x) is complex:
+            return f_complex(x)
+        try:
+            x = float(x)
+            return f_real(x)
+        except (TypeError, ValueError):
+            x = complex(x)
+            return f_complex(x)
+    f.__name__ = f_real.__name__
+    return f
+
+def _mathfun(f_real, f_complex):
+    def f(x, **kwargs):
+        if type(x) is complex:
+            return f_complex(x)
+        try:
+            return f_real(float(x))
+        except (TypeError, ValueError):
+            return f_complex(complex(x))
+    f.__name__ = f_real.__name__
+    return f
+
+def _mathfun_n(f_real, f_complex):
+    def f(*args, **kwargs):
+        try:
+            return f_real(*(float(x) for x in args))
+        except (TypeError, ValueError):
+            return f_complex(*(complex(x) for x in args))
+    f.__name__ = f_real.__name__
+    return f
+
+# Workaround for non-raising log and sqrt in Python 2.5 and 2.4
+# on Unix system
+try:
+    math.log(-2.0)
+    def math_log(x):
+        if x <= 0.0:
+            raise ValueError("math domain error")
+        return math.log(x)
+    def math_sqrt(x):
+        if x < 0.0:
+            raise ValueError("math domain error")
+        return math.sqrt(x)
+except (ValueError, TypeError):
+    math_log = math.log
+    math_sqrt = math.sqrt
+
+pow = _mathfun_n(operator.pow, lambda x, y: complex(x)**y)
+log = _mathfun_n(math_log, cmath.log)
+sqrt = _mathfun(math_sqrt, cmath.sqrt)
+exp = _mathfun_real(math.exp, cmath.exp)
+
+cos = _mathfun_real(math.cos, cmath.cos)
+sin = _mathfun_real(math.sin, cmath.sin)
+tan = _mathfun_real(math.tan, cmath.tan)
+
+acos = _mathfun(math.acos, cmath.acos)
+asin = _mathfun(math.asin, cmath.asin)
+atan = _mathfun_real(math.atan, cmath.atan)
+
+cosh = _mathfun_real(math.cosh, cmath.cosh)
+sinh = _mathfun_real(math.sinh, cmath.sinh)
+tanh = _mathfun_real(math.tanh, cmath.tanh)
+
+floor = _mathfun_real(math.floor,
+    lambda z: complex(math.floor(z.real), math.floor(z.imag)))
+ceil = _mathfun_real(math.ceil,
+    lambda z: complex(math.ceil(z.real), math.ceil(z.imag)))
+
+
+cos_sin = _mathfun_real(lambda x: (math.cos(x), math.sin(x)),
+                        lambda z: (cmath.cos(z), cmath.sin(z)))
+
+cbrt = _mathfun(lambda x: x**(1./3), lambda z: z**(1./3))
+
+def nthroot(x, n):
+    r = 1./n
+    try:
+        return float(x) ** r
+    except (ValueError, TypeError):
+        return complex(x) ** r
+
+def _sinpi_real(x):
+    if x < 0:
+        return -_sinpi_real(-x)
+    n, r = divmod(x, 0.5)
+    r *= pi
+    n %= 4
+    if n == 0: return math.sin(r)
+    if n == 1: return math.cos(r)
+    if n == 2: return -math.sin(r)
+    if n == 3: return -math.cos(r)
+
+def _cospi_real(x):
+    if x < 0:
+        x = -x
+    n, r = divmod(x, 0.5)
+    r *= pi
+    n %= 4
+    if n == 0: return math.cos(r)
+    if n == 1: return -math.sin(r)
+    if n == 2: return -math.cos(r)
+    if n == 3: return math.sin(r)
+
+def _sinpi_complex(z):
+    if z.real < 0:
+        return -_sinpi_complex(-z)
+    n, r = divmod(z.real, 0.5)
+    z = pi*complex(r, z.imag)
+    n %= 4
+    if n == 0: return cmath.sin(z)
+    if n == 1: return cmath.cos(z)
+    if n == 2: return -cmath.sin(z)
+    if n == 3: return -cmath.cos(z)
+
+def _cospi_complex(z):
+    if z.real < 0:
+        z = -z
+    n, r = divmod(z.real, 0.5)
+    z = pi*complex(r, z.imag)
+    n %= 4
+    if n == 0: return cmath.cos(z)
+    if n == 1: return -cmath.sin(z)
+    if n == 2: return -cmath.cos(z)
+    if n == 3: return cmath.sin(z)
+
+cospi = _mathfun_real(_cospi_real, _cospi_complex)
+sinpi = _mathfun_real(_sinpi_real, _sinpi_complex)
+
+def tanpi(x):
+    try:
+        return sinpi(x) / cospi(x)
+    except OverflowError:
+        if complex(x).imag > 10:
+            return 1j
+        if complex(x).imag < 10:
+            return -1j
+        raise
+
+def cotpi(x):
+    try:
+        return cospi(x) / sinpi(x)
+    except OverflowError:
+        if complex(x).imag > 10:
+            return -1j
+        if complex(x).imag < 10:
+            return 1j
+        raise
+
+INF = 1e300*1e300
+NINF = -INF
+NAN = INF-INF
+EPS = 2.2204460492503131e-16
+
+_exact_gamma = (INF, 1.0, 1.0, 2.0, 6.0, 24.0, 120.0, 720.0, 5040.0, 40320.0,
+  362880.0, 3628800.0, 39916800.0, 479001600.0, 6227020800.0, 87178291200.0,
+  1307674368000.0, 20922789888000.0, 355687428096000.0, 6402373705728000.0,
+  121645100408832000.0, 2432902008176640000.0)
+
+_max_exact_gamma = len(_exact_gamma)-1
+
+# Lanczos coefficients used by the GNU Scientific Library
+_lanczos_g = 7
+_lanczos_p = (0.99999999999980993, 676.5203681218851, -1259.1392167224028,
+     771.32342877765313, -176.61502916214059, 12.507343278686905,
+     -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7)
+
+def _gamma_real(x):
+    _intx = int(x)
+    if _intx == x:
+        if _intx <= 0:
+            #return (-1)**_intx * INF
+            raise ZeroDivisionError("gamma function pole")
+        if _intx <= _max_exact_gamma:
+            return _exact_gamma[_intx]
+    if x < 0.5:
+        # TODO: sinpi
+        return pi / (_sinpi_real(x)*_gamma_real(1-x))
+    else:
+        x -= 1.0
+        r = _lanczos_p[0]
+        for i in range(1, _lanczos_g+2):
+            r += _lanczos_p[i]/(x+i)
+        t = x + _lanczos_g + 0.5
+        return 2.506628274631000502417 * t**(x+0.5) * math.exp(-t) * r
+
+def _gamma_complex(x):
+    if not x.imag:
+        return complex(_gamma_real(x.real))
+    if x.real < 0.5:
+        # TODO: sinpi
+        return pi / (_sinpi_complex(x)*_gamma_complex(1-x))
+    else:
+        x -= 1.0
+        r = _lanczos_p[0]
+        for i in range(1, _lanczos_g+2):
+            r += _lanczos_p[i]/(x+i)
+        t = x + _lanczos_g + 0.5
+        return 2.506628274631000502417 * t**(x+0.5) * cmath.exp(-t) * r
+
+gamma = _mathfun_real(_gamma_real, _gamma_complex)
+
+def rgamma(x):
+    try:
+        return 1./gamma(x)
+    except ZeroDivisionError:
+        return x*0.0
+
+def factorial(x):
+    return gamma(x+1.0)
+
+def arg(x):
+    if type(x) is float:
+        return math.atan2(0.0,x)
+    return math.atan2(x.imag,x.real)
+
+# XXX: broken for negatives
+def loggamma(x):
+    if type(x) not in (float, complex):
+        try:
+            x = float(x)
+        except (ValueError, TypeError):
+            x = complex(x)
+    try:
+        xreal = x.real
+        ximag = x.imag
+    except AttributeError:   # py2.5
+        xreal = x
+        ximag = 0.0
+    # Reflection formula
+    # http://functions.wolfram.com/GammaBetaErf/LogGamma/16/01/01/0003/
+    if xreal < 0.0:
+        if abs(x) < 0.5:
+            v = log(gamma(x))
+            if ximag == 0:
+                v = v.conjugate()
+            return v
+        z = 1-x
+        try:
+            re = z.real
+            im = z.imag
+        except AttributeError:   # py2.5
+            re = z
+            im = 0.0
+        refloor = floor(re)
+        if im == 0.0:
+            imsign = 0
+        elif im < 0.0:
+            imsign = -1
+        else:
+            imsign = 1
+        return (-pi*1j)*abs(refloor)*(1-abs(imsign)) + logpi - \
+            log(sinpi(z-refloor)) - loggamma(z) + 1j*pi*refloor*imsign
+    if x == 1.0 or x == 2.0:
+        return x*0
+    p = 0.
+    while abs(x) < 11:
+        p -= log(x)
+        x += 1.0
+    s = 0.918938533204672742 + (x-0.5)*log(x) - x
+    r = 1./x
+    r2 = r*r
+    s += 0.083333333333333333333*r; r *= r2
+    s += -0.0027777777777777777778*r; r *= r2
+    s += 0.00079365079365079365079*r; r *= r2
+    s += -0.0005952380952380952381*r; r *= r2
+    s += 0.00084175084175084175084*r; r *= r2
+    s += -0.0019175269175269175269*r; r *= r2
+    s += 0.0064102564102564102564*r; r *= r2
+    s += -0.02955065359477124183*r
+    return s + p
+
+_psi_coeff = [
+0.083333333333333333333,
+-0.0083333333333333333333,
+0.003968253968253968254,
+-0.0041666666666666666667,
+0.0075757575757575757576,
+-0.021092796092796092796,
+0.083333333333333333333,
+-0.44325980392156862745,
+3.0539543302701197438,
+-26.456212121212121212]
+
+def _digamma_real(x):
+    _intx = int(x)
+    if _intx == x:
+        if _intx <= 0:
+            raise ZeroDivisionError("polygamma pole")
+    if x < 0.5:
+        x = 1.0-x
+        s = pi*cotpi(x)
+    else:
+        s = 0.0
+    while x < 10.0:
+        s -= 1.0/x
+        x += 1.0
+    x2 = x**-2
+    t = x2
+    for c in _psi_coeff:
+        s -= c*t
+        if t < 1e-20:
+            break
+        t *= x2
+    return s + math_log(x) - 0.5/x
+
+def _digamma_complex(x):
+    if not x.imag:
+        return complex(_digamma_real(x.real))
+    if x.real < 0.5:
+        x = 1.0-x
+        s = pi*cotpi(x)
+    else:
+        s = 0.0
+    while abs(x) < 10.0:
+        s -= 1.0/x
+        x += 1.0
+    x2 = x**-2
+    t = x2
+    for c in _psi_coeff:
+        s -= c*t
+        if abs(t) < 1e-20:
+            break
+        t *= x2
+    return s + cmath.log(x) - 0.5/x
+
+digamma = _mathfun_real(_digamma_real, _digamma_complex)
+
+# TODO: could implement complex erf and erfc here. Need
+# to find an accurate method (avoiding cancellation)
+# for approx. 1 < abs(x) < 9.
+
+_erfc_coeff_P = [
+    1.0000000161203922312,
+    2.1275306946297962644,
+    2.2280433377390253297,
+    1.4695509105618423961,
+    0.66275911699770787537,
+    0.20924776504163751585,
+    0.045459713768411264339,
+    0.0063065951710717791934,
+    0.00044560259661560421715][::-1]
+
+_erfc_coeff_Q = [
+    1.0000000000000000000,
+    3.2559100272784894318,
+    4.9019435608903239131,
+    4.4971472894498014205,
+    2.7845640601891186528,
+    1.2146026030046904138,
+    0.37647108453729465912,
+    0.080970149639040548613,
+    0.011178148899483545902,
+    0.00078981003831980423513][::-1]
+
+def _polyval(coeffs, x):
+    p = coeffs[0]
+    for c in coeffs[1:]:
+        p = c + x*p
+    return p
+
+def _erf_taylor(x):
+    # Taylor series assuming 0 <= x <= 1
+    x2 = x*x
+    s = t = x
+    n = 1
+    while abs(t) > 1e-17:
+        t *= x2/n
+        s -= t/(n+n+1)
+        n += 1
+        t *= x2/n
+        s += t/(n+n+1)
+        n += 1
+    return 1.1283791670955125739*s
+
+def _erfc_mid(x):
+    # Rational approximation assuming 0 <= x <= 9
+    return exp(-x*x)*_polyval(_erfc_coeff_P,x)/_polyval(_erfc_coeff_Q,x)
+
+def _erfc_asymp(x):
+    # Asymptotic expansion assuming x >= 9
+    x2 = x*x
+    v = exp(-x2)/x*0.56418958354775628695
+    r = t = 0.5 / x2
+    s = 1.0
+    for n in range(1,22,4):
+        s -= t
+        t *= r * (n+2)
+        s += t
+        t *= r * (n+4)
+        if abs(t) < 1e-17:
+            break
+    return s * v
+
+def erf(x):
+    """
+    erf of a real number.
+    """
+    x = float(x)
+    if x != x:
+        return x
+    if x < 0.0:
+        return -erf(-x)
+    if x >= 1.0:
+        if x >= 6.0:
+            return 1.0
+        return 1.0 - _erfc_mid(x)
+    return _erf_taylor(x)
+
+def erfc(x):
+    """
+    erfc of a real number.
+    """
+    x = float(x)
+    if x != x:
+        return x
+    if x < 0.0:
+        if x < -6.0:
+            return 2.0
+        return 2.0-erfc(-x)
+    if x > 9.0:
+        return _erfc_asymp(x)
+    if x >= 1.0:
+        return _erfc_mid(x)
+    return 1.0 - _erf_taylor(x)
+
+gauss42 = [\
+(0.99839961899006235, 0.0041059986046490839),
+(-0.99839961899006235, 0.0041059986046490839),
+(0.9915772883408609, 0.009536220301748501),
+(-0.9915772883408609,0.009536220301748501),
+(0.97934250806374812, 0.014922443697357493),
+(-0.97934250806374812, 0.014922443697357493),
+(0.96175936533820439,0.020227869569052644),
+(-0.96175936533820439, 0.020227869569052644),
+(0.93892355735498811, 0.025422959526113047),
+(-0.93892355735498811,0.025422959526113047),
+(0.91095972490412735, 0.030479240699603467),
+(-0.91095972490412735, 0.030479240699603467),
+(0.87802056981217269,0.03536907109759211),
+(-0.87802056981217269, 0.03536907109759211),
+(0.8402859832618168, 0.040065735180692258),
+(-0.8402859832618168,0.040065735180692258),
+(0.7979620532554873, 0.044543577771965874),
+(-0.7979620532554873, 0.044543577771965874),
+(0.75127993568948048,0.048778140792803244),
+(-0.75127993568948048, 0.048778140792803244),
+(0.70049459055617114, 0.052746295699174064),
+(-0.70049459055617114,0.052746295699174064),
+(0.64588338886924779, 0.056426369358018376),
+(-0.64588338886924779, 0.056426369358018376),
+(0.58774459748510932, 0.059798262227586649),
+(-0.58774459748510932, 0.059798262227586649),
+(0.5263957499311922, 0.062843558045002565),
+(-0.5263957499311922, 0.062843558045002565),
+(0.46217191207042191, 0.065545624364908975),
+(-0.46217191207042191, 0.065545624364908975),
+(0.39542385204297503, 0.067889703376521934),
+(-0.39542385204297503, 0.067889703376521934),
+(0.32651612446541151, 0.069862992492594159),
+(-0.32651612446541151, 0.069862992492594159),
+(0.25582507934287907, 0.071454714265170971),
+(-0.25582507934287907, 0.071454714265170971),
+(0.18373680656485453, 0.072656175243804091),
+(-0.18373680656485453, 0.072656175243804091),
+(0.11064502720851986, 0.073460813453467527),
+(-0.11064502720851986, 0.073460813453467527),
+(0.036948943165351772, 0.073864234232172879),
+(-0.036948943165351772, 0.073864234232172879)]
+
+EI_ASYMP_CONVERGENCE_RADIUS = 40.0
+
+def ei_asymp(z, _e1=False):
+    r = 1./z
+    s = t = 1.0
+    k = 1
+    while 1:
+        t *= k*r
+        s += t
+        if abs(t) < 1e-16:
+            break
+        k += 1
+    v = s*exp(z)/z
+    if _e1:
+        if type(z) is complex:
+            zreal = z.real
+            zimag = z.imag
+        else:
+            zreal = z
+            zimag = 0.0
+        if zimag == 0.0 and zreal > 0.0:
+            v += pi*1j
+    else:
+        if type(z) is complex:
+            if z.imag > 0:
+                v += pi*1j
+            if z.imag < 0:
+                v -= pi*1j
+    return v
+
+def ei_taylor(z, _e1=False):
+    s = t = z
+    k = 2
+    while 1:
+        t = t*z/k
+        term = t/k
+        if abs(term) < 1e-17:
+            break
+        s += term
+        k += 1
+    s += euler
+    if _e1:
+        s += log(-z)
+    else:
+        if type(z) is float or z.imag == 0.0:
+            s += math_log(abs(z))
+        else:
+            s += cmath.log(z)
+    return s
+
+def ei(z, _e1=False):
+    typez = type(z)
+    if typez not in (float, complex):
+        try:
+            z = float(z)
+            typez = float
+        except (TypeError, ValueError):
+            z = complex(z)
+            typez = complex
+    if not z:
+        return -INF
+    absz = abs(z)
+    if absz > EI_ASYMP_CONVERGENCE_RADIUS:
+        return ei_asymp(z, _e1)
+    elif absz <= 2.0 or (typez is float and z > 0.0):
+        return ei_taylor(z, _e1)
+    # Integrate, starting from whichever is smaller of a Taylor
+    # series value or an asymptotic series value
+    if typez is complex and z.real > 0.0:
+        zref = z / absz
+        ref = ei_taylor(zref, _e1)
+    else:
+        zref = EI_ASYMP_CONVERGENCE_RADIUS * z / absz
+        ref = ei_asymp(zref, _e1)
+    C = (zref-z)*0.5
+    D = (zref+z)*0.5
+    s = 0.0
+    if type(z) is complex:
+        _exp = cmath.exp
+    else:
+        _exp = math.exp
+    for x,w in gauss42:
+        t = C*x+D
+        s += w*_exp(t)/t
+    ref -= C*s
+    return ref
+
+def e1(z):
+    # hack to get consistent signs if the imaginary part if 0
+    # and signed
+    typez = type(z)
+    if type(z) not in (float, complex):
+        try:
+            z = float(z)
+            typez = float
+        except (TypeError, ValueError):
+            z = complex(z)
+            typez = complex
+    if typez is complex and not z.imag:
+        z = complex(z.real, 0.0)
+    # end hack
+    return -ei(-z, _e1=True)
+
+_zeta_int = [\
+-0.5,
+0.0,
+1.6449340668482264365,1.2020569031595942854,1.0823232337111381915,
+1.0369277551433699263,1.0173430619844491397,1.0083492773819228268,
+1.0040773561979443394,1.0020083928260822144,1.0009945751278180853,
+1.0004941886041194646,1.0002460865533080483,1.0001227133475784891,
+1.0000612481350587048,1.0000305882363070205,1.0000152822594086519,
+1.0000076371976378998,1.0000038172932649998,1.0000019082127165539,
+1.0000009539620338728,1.0000004769329867878,1.0000002384505027277,
+1.0000001192199259653,1.0000000596081890513,1.0000000298035035147,
+1.0000000149015548284]
+
+_zeta_P = [-3.50000000087575873, -0.701274355654678147,
+-0.0672313458590012612, -0.00398731457954257841,
+-0.000160948723019303141, -4.67633010038383371e-6,
+-1.02078104417700585e-7, -1.68030037095896287e-9,
+-1.85231868742346722e-11][::-1]
+
+_zeta_Q = [1.00000000000000000, -0.936552848762465319,
+-0.0588835413263763741, -0.00441498861482948666,
+-0.000143416758067432622, -5.10691659585090782e-6,
+-9.58813053268913799e-8, -1.72963791443181972e-9,
+-1.83527919681474132e-11][::-1]
+
+_zeta_1 = [3.03768838606128127e-10, -1.21924525236601262e-8,
+2.01201845887608893e-7, -1.53917240683468381e-6,
+-5.09890411005967954e-7, 0.000122464707271619326,
+-0.000905721539353130232, -0.00239315326074843037,
+0.084239750013159168, 0.418938517907442414, 0.500000001921884009]
+
+_zeta_0 = [-3.46092485016748794e-10, -6.42610089468292485e-9,
+1.76409071536679773e-7, -1.47141263991560698e-6, -6.38880222546167613e-7,
+0.000122641099800668209, -0.000905894913516772796, -0.00239303348507992713,
+0.0842396947501199816, 0.418938533204660256, 0.500000000000000052]
+
+def zeta(s):
+    """
+    Riemann zeta function, real argument
+    """
+    if not isinstance(s, (float, int)):
+        try:
+            s = float(s)
+        except (ValueError, TypeError):
+            try:
+                s = complex(s)
+                if not s.imag:
+                    return complex(zeta(s.real))
+            except (ValueError, TypeError):
+                pass
+            raise NotImplementedError
+    if s == 1:
+        raise ValueError("zeta(1) pole")
+    if s >= 27:
+        return 1.0 + 2.0**(-s) + 3.0**(-s)
+    n = int(s)
+    if n == s:
+        if n >= 0:
+            return _zeta_int[n]
+        if not (n % 2):
+            return 0.0
+    if s <= 0.0:
+        return 2.**s*pi**(s-1)*_sinpi_real(0.5*s)*_gamma_real(1-s)*zeta(1-s)
+    if s <= 2.0:
+        if s <= 1.0:
+            return _polyval(_zeta_0,s)/(s-1)
+        return _polyval(_zeta_1,s)/(s-1)
+    z = _polyval(_zeta_P,s) / _polyval(_zeta_Q,s)
+    return 1.0 + 2.0**(-s) + 3.0**(-s) + 4.0**(-s)*z

venv/lib/python3.10/site-packages/mpmath/rational.py

@@ -0,0 +1,240 @@
+import operator
+import sys
+from .libmp import int_types, mpf_hash, bitcount, from_man_exp, HASH_MODULUS
+
+new = object.__new__
+
+def create_reduced(p, q, _cache={}):
+    key = p, q
+    if key in _cache:
+        return _cache[key]
+    x, y = p, q
+    while y:
+        x, y = y, x % y
+    if x != 1:
+        p //= x
+        q //= x
+    v = new(mpq)
+    v._mpq_ = p, q
+    # Speedup integers, half-integers and other small fractions
+    if q <= 4 and abs(key[0]) < 100:
+        _cache[key] = v
+    return v
+
+class mpq(object):
+    """
+    Exact rational type, currently only intended for internal use.
+    """
+
+    __slots__ = ["_mpq_"]
+
+    def __new__(cls, p, q=1):
+        if type(p) is tuple:
+            p, q = p
+        elif hasattr(p, '_mpq_'):
+            p, q = p._mpq_
+        return create_reduced(p, q)
+
+    def __repr__(s):
+        return "mpq(%s,%s)" % s._mpq_
+
+    def __str__(s):
+        return "(%s/%s)" % s._mpq_
+
+    def __int__(s):
+        a, b = s._mpq_
+        return a // b
+
+    def __nonzero__(s):
+        return bool(s._mpq_[0])
+
+    __bool__ = __nonzero__
+
+    def __hash__(s):
+        a, b = s._mpq_
+        if sys.version_info >= (3, 2):
+            inverse = pow(b, HASH_MODULUS-2, HASH_MODULUS)
+            if not inverse:
+                h = sys.hash_info.inf
+            else:
+                h = (abs(a) * inverse) % HASH_MODULUS
+            if a < 0: h = -h
+            if h == -1: h = -2
+            return h
+        else:
+            if b == 1:
+                return hash(a)
+            # Power of two: mpf compatible hash
+            if not (b & (b-1)):
+                return mpf_hash(from_man_exp(a, 1-bitcount(b)))
+            return hash((a,b))
+
+    def __eq__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            return s._mpq_ == t._mpq_
+        if ttype in int_types:
+            a, b = s._mpq_
+            if b != 1:
+                return False
+            return a == t
+        return NotImplemented
+
+    def __ne__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            return s._mpq_ != t._mpq_
+        if ttype in int_types:
+            a, b = s._mpq_
+            if b != 1:
+                return True
+            return a != t
+        return NotImplemented
+
+    def _cmp(s, t, op):
+        ttype = type(t)
+        if ttype in int_types:
+            a, b = s._mpq_
+            return op(a, t*b)
+        if ttype is mpq:
+            a, b = s._mpq_
+            c, d = t._mpq_
+            return op(a*d, b*c)
+        return NotImplementedError
+
+    def __lt__(s, t): return s._cmp(t, operator.lt)
+    def __le__(s, t): return s._cmp(t, operator.le)
+    def __gt__(s, t): return s._cmp(t, operator.gt)
+    def __ge__(s, t): return s._cmp(t, operator.ge)
+
+    def __abs__(s):
+        a, b = s._mpq_
+        if a >= 0:
+            return s
+        v = new(mpq)
+        v._mpq_ = -a, b
+        return v
+
+    def __neg__(s):
+        a, b = s._mpq_
+        v = new(mpq)
+        v._mpq_ = -a, b
+        return v
+
+    def __pos__(s):
+        return s
+
+    def __add__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            a, b = s._mpq_
+            c, d = t._mpq_
+            return create_reduced(a*d+b*c, b*d)
+        if ttype in int_types:
+            a, b = s._mpq_
+            v = new(mpq)
+            v._mpq_ = a+b*t, b
+            return v
+        return NotImplemented
+
+    __radd__ = __add__
+
+    def __sub__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            a, b = s._mpq_
+            c, d = t._mpq_
+            return create_reduced(a*d-b*c, b*d)
+        if ttype in int_types:
+            a, b = s._mpq_
+            v = new(mpq)
+            v._mpq_ = a-b*t, b
+            return v
+        return NotImplemented
+
+    def __rsub__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            a, b = s._mpq_
+            c, d = t._mpq_
+            return create_reduced(b*c-a*d, b*d)
+        if ttype in int_types:
+            a, b = s._mpq_
+            v = new(mpq)
+            v._mpq_ = b*t-a, b
+            return v
+        return NotImplemented
+
+    def __mul__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            a, b = s._mpq_
+            c, d = t._mpq_
+            return create_reduced(a*c, b*d)
+        if ttype in int_types:
+            a, b = s._mpq_
+            return create_reduced(a*t, b)
+        return NotImplemented
+
+    __rmul__ = __mul__
+
+    def __div__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            a, b = s._mpq_
+            c, d = t._mpq_
+            return create_reduced(a*d, b*c)
+        if ttype in int_types:
+            a, b = s._mpq_
+            return create_reduced(a, b*t)
+        return NotImplemented
+
+    def __rdiv__(s, t):
+        ttype = type(t)
+        if ttype is mpq:
+            a, b = s._mpq_
+            c, d = t._mpq_
+            return create_reduced(b*c, a*d)
+        if ttype in int_types:
+            a, b = s._mpq_
+            return create_reduced(b*t, a)
+        return NotImplemented
+
+    def __pow__(s, t):
+        ttype = type(t)
+        if ttype in int_types:
+            a, b = s._mpq_
+            if t:
+                if t < 0:
+                    a, b, t = b, a, -t
+                v = new(mpq)
+                v._mpq_ = a**t, b**t
+                return v
+            raise ZeroDivisionError
+        return NotImplemented
+
+
+mpq_1 = mpq((1,1))
+mpq_0 = mpq((0,1))
+mpq_1_2 = mpq((1,2))
+mpq_3_2 = mpq((3,2))
+mpq_1_4 = mpq((1,4))
+mpq_1_16 = mpq((1,16))
+mpq_3_16 = mpq((3,16))
+mpq_5_2 = mpq((5,2))
+mpq_3_4 = mpq((3,4))
+mpq_7_4 = mpq((7,4))
+mpq_5_4 = mpq((5,4))
+
+
+# Register with "numbers" ABC
+#     We do not subclass, hence we do not use the @abstractmethod checks. While
+#     this is less invasive it may turn out that we do not actually support
+#     parts of the expected interfaces.  See
+#     http://docs.python.org/2/library/numbers.html for list of abstract
+#     methods.
+try:
+    import numbers
+    numbers.Rational.register(mpq)
+except ImportError:
+    pass