text: """ define the IntervalIndex """
  import textwrap
  import warnings
  
  import numpy as np
  
  from pandas._config import get_option
  
  from pandas._libs import Timedelta, Timestamp
  from pandas._libs.interval import Interval, IntervalMixin, IntervalTree
  from pandas.util._decorators import Appender, Substitution, cache_readonly
  from pandas.util._exceptions import rewrite_exception
  
  from pandas.core.dtypes.cast import (
      find_common_type, infer_dtype_from_scalar, maybe_downcast_to_dtype)
  from pandas.core.dtypes.common import (
      ensure_platform_int, is_datetime64tz_dtype, is_datetime_or_timedelta_dtype,
      is_dtype_equal, is_float, is_float_dtype, is_integer, is_integer_dtype,
      is_interval_dtype, is_list_like, is_number, is_object_dtype, is_scalar)
  from pandas.core.dtypes.missing import isna
  
  from pandas.core.arrays.interval import IntervalArray, _interval_shared_docs
  import pandas.core.common as com
  import pandas.core.indexes.base as ibase
  from pandas.core.indexes.base import (
      Index, _index_shared_docs, default_pprint, ensure_index)
  from pandas.core.indexes.datetimes import DatetimeIndex, date_range
  from pandas.core.indexes.multi import MultiIndex
  from pandas.core.indexes.timedeltas import TimedeltaIndex, timedelta_range
  from pandas.core.ops import get_op_result_name
  
  from pandas.tseries.frequencies import to_offset
  from pandas.tseries.offsets import DateOffset
  
  _VALID_CLOSED = {'left', 'right', 'both', 'neither'}
  _index_doc_kwargs = dict(ibase._index_doc_kwargs)
  
  _index_doc_kwargs.update(
      dict(klass='IntervalIndex',
           qualname="IntervalIndex",
           target_klass='IntervalIndex or list of Intervals',
           name=textwrap.dedent("""\
           name : object, optional
                Name to be stored in the index.
           """),
           ))
  
  
  def _get_next_label(label):
      dtype = getattr(label, 'dtype', type(label))
      if isinstance(label, (Timestamp, Timedelta)):
          dtype = 'datetime64'
      if is_datetime_or_timedelta_dtype(dtype) or is_datetime64tz_dtype(dtype):
          return label + np.timedelta64(1, 'ns')
      elif is_integer_dtype(dtype):
          return label + 1
      elif is_float_dtype(dtype):
          return np.nextafter(label, np.infty)
      else:
          raise TypeError('cannot determine next label for type {typ!r}'
                          .format(typ=type(label)))
  
  
  def _get_prev_label(label):
      dtype = getattr(label, 'dtype', type(label))
      if isinstance(label, (Timestamp, Timedelta)):
          dtype = 'datetime64'
      if is_datetime_or_timedelta_dtype(dtype) or is_datetime64tz_dtype(dtype):
          return label - np.timedelta64(1, 'ns')
      elif is_integer_dtype(dtype):
          return label - 1
      elif is_float_dtype(dtype):
          return np.nextafter(label, -np.infty)
      else:
          raise TypeError('cannot determine next label for type {typ!r}'
                          .format(typ=type(label)))
  
  
  def _get_interval_closed_bounds(interval):
      """
      Given an Interval or IntervalIndex, return the corresponding interval with
      closed bounds.
      """
      left, right = interval.left, interval.right
      if interval.open_left:
          left = _get_next_label(left)
      if interval.open_right:
          right = _get_prev_label(right)
      return left, right
  
  
  def _new_IntervalIndex(cls, d):
      """
      This is called upon unpickling, rather than the default which doesn't have
      arguments and breaks __new__
      """
      return cls.from_arrays(**d)
  
  
  class SetopCheck:
      """
      This is called to decorate the set operations of IntervalIndex
      to perform the type check in advance.
      """
      def __init__(self, op_name):
          self.op_name = op_name
  
      def __call__(self, setop):
          def func(intvidx_self, other, sort=False):
              intvidx_self._assert_can_do_setop(other)
              other = ensure_index(other)
  
              if not isinstance(other, IntervalIndex):
                  result = getattr(intvidx_self.astype(object),
                                   self.op_name)(other)
                  if self.op_name in ('difference',):
                      result = result.astype(intvidx_self.dtype)
                  return result
              elif intvidx_self.closed != other.closed:
                  msg = ('can only do set operations between two IntervalIndex '
                         'objects that are closed on the same side')
                  raise ValueError(msg)
  
              # GH 19016: ensure set op will not return a prohibited dtype
              subtypes = [intvidx_self.dtype.subtype, other.dtype.subtype]
              common_subtype = find_common_type(subtypes)
              if is_object_dtype(common_subtype):
                  msg = ('can only do {op} between two IntervalIndex '
                         'objects that have compatible dtypes')
                  raise TypeError(msg.format(op=self.op_name))
  
              return setop(intvidx_self, other, sort)
          return func
  
  
  @Appender(_interval_shared_docs['class'] % dict(
      klass="IntervalIndex",
      summary="Immutable index of intervals that are closed on the same side.",
      name=_index_doc_kwargs['name'],
      versionadded="0.20.0",
      extra_attributes="is_overlapping\nvalues\n",
      extra_methods="contains\n",
      examples=textwrap.dedent("""\
      Examples
      --------
      A new ``IntervalIndex`` is typically constructed using
      :func:`interval_range`:
  
      >>> pd.interval_range(start=0, end=5)
      IntervalIndex([(0, 1], (1, 2], (2, 3], (3, 4], (4, 5]],
                    closed='right',
                    dtype='interval[int64]')
  
      It may also be constructed using one of the constructor
      methods: :meth:`IntervalIndex.from_arrays`,
      :meth:`IntervalIndex.from_breaks`, and :meth:`IntervalIndex.from_tuples`.
  
      See further examples in the doc strings of ``interval_range`` and the
      mentioned constructor methods.
      """),
  
  ))
  class IntervalIndex(IntervalMixin, Index):
      _typ = 'intervalindex'
      _comparables = ['name']
      _attributes = ['name', 'closed']
  
      # we would like our indexing holder to defer to us
      _defer_to_indexing = True
  
      # Immutable, so we are able to cache computations like isna in '_mask'
      _mask = None
  
      # --------------------------------------------------------------------
      # Constructors
  
      def __new__(cls, data, closed=None, dtype=None, copy=False,
                  name=None, verify_integrity=True):
  
          if name is None and hasattr(data, 'name'):
              name = data.name
  
          with rewrite_exception("IntervalArray", cls.__name__):
              array = IntervalArray(data, closed=closed, copy=copy, dtype=dtype,
                                    verify_integrity=verify_integrity)
  
          return cls._simple_new(array, name)
  
      @classmethod
      def _simple_new(cls, array, name, closed=None):
          """
          Construct from an IntervalArray
  
          Parameters
          ----------
          array : IntervalArray
          name : str
              Attached as result.name
          closed : Any
              Ignored.
          """
          result = IntervalMixin.__new__(cls)
          result._data = array
          result.name = name
          result._reset_identity()
          return result
  
      @classmethod
      @Appender(_interval_shared_docs['from_breaks'] % _index_doc_kwargs)
      def from_breaks(cls, breaks, closed='right', name=None, copy=False,
                      dtype=None):
          with rewrite_exception("IntervalArray", cls.__name__):
              array = IntervalArray.from_breaks(breaks, closed=closed, copy=copy,
                                                dtype=dtype)
          return cls._simple_new(array, name=name)
  
      @classmethod
      @Appender(_interval_shared_docs['from_arrays'] % _index_doc_kwargs)
      def from_arrays(cls, left, right, closed='right', name=None, copy=False,
                      dtype=None):
          with rewrite_exception("IntervalArray", cls.__name__):
              array = IntervalArray.from_arrays(left, right, closed, copy=copy,
                                                dtype=dtype)
          return cls._simple_new(array, name=name)
  
      @classmethod
      @Appender(_interval_shared_docs['from_intervals'] % _index_doc_kwargs)
      def from_intervals(cls, data, closed=None, name=None, copy=False,
                         dtype=None):
          msg = ('IntervalIndex.from_intervals is deprecated and will be '
                 'removed in a future version; Use IntervalIndex(...) instead')
          warnings.warn(msg, FutureWarning, stacklevel=2)
          with rewrite_exception("IntervalArray", cls.__name__):
              array = IntervalArray(data, closed=closed, copy=copy, dtype=dtype)
  
          if name is None and isinstance(data, cls):
              name = data.name
  
          return cls._simple_new(array, name=name)
  
      @classmethod
      @Appender(_interval_shared_docs['from_tuples'] % _index_doc_kwargs)
      def from_tuples(cls, data, closed='right', name=None, copy=False,
                      dtype=None):
          with rewrite_exception("IntervalArray", cls.__name__):
              arr = IntervalArray.from_tuples(data, closed=closed, copy=copy,
                                              dtype=dtype)
          return cls._simple_new(arr, name=name)
  
      # --------------------------------------------------------------------
  
      @Appender(_index_shared_docs['_shallow_copy'])
      def _shallow_copy(self, left=None, right=None, **kwargs):
          result = self._data._shallow_copy(left=left, right=right)
          attributes = self._get_attributes_dict()
          attributes.update(kwargs)
          return self._simple_new(result, **attributes)
  
      @cache_readonly
      def _isnan(self):
          """Return a mask indicating if each value is NA"""
          if self._mask is None:
              self._mask = isna(self.left)
          return self._mask
  
      @cache_readonly
      def _engine(self):
          left = self._maybe_convert_i8(self.left)
          right = self._maybe_convert_i8(self.right)
          return IntervalTree(left, right, closed=self.closed)
  
      def __contains__(self, key):
          """
          return a boolean if this key is IN the index
          We *only* accept an Interval
  
          Parameters
          ----------
          key : Interval
  
          Returns
          -------
          boolean
          """
          if not isinstance(key, Interval):
              return False
  
          try:
              self.get_loc(key)
              return True
          except KeyError:
              return False
  
      def contains(self, key):
          """
          Return a boolean indicating if the key is IN the index
  
          We accept / allow keys to be not *just* actual
          objects.
  
          Parameters
          ----------
          key : int, float, Interval
  
          Returns
          -------
          boolean
          """
          try:
              self.get_loc(key)
              return True
          except KeyError:
              return False
  
      @Appender(_interval_shared_docs['to_tuples'] % dict(
          return_type="Index",
          examples="""
          Examples
          --------
          >>> idx = pd.IntervalIndex.from_arrays([0, np.nan, 2], [1, np.nan, 3])
          >>> idx.to_tuples()
          Index([(0.0, 1.0), (nan, nan), (2.0, 3.0)], dtype='object')
          >>> idx.to_tuples(na_tuple=False)
          Index([(0.0, 1.0), nan, (2.0, 3.0)], dtype='object')""",
      ))
      def to_tuples(self, na_tuple=True):
          tuples = self._data.to_tuples(na_tuple=na_tuple)
          return Index(tuples)
  
      @cache_readonly
      def _multiindex(self):
          return MultiIndex.from_arrays([self.left, self.right],
                                        names=['left', 'right'])
  
      @property
      def left(self):
          """
          Return the left endpoints of each Interval in the IntervalIndex as
          an Index
          """
          return self._data._left
  
      @property
      def right(self):
          """
          Return the right endpoints of each Interval in the IntervalIndex as
          an Index
          """
          return self._data._right
  
      @property
      def closed(self):
          """
          Whether the intervals are closed on the left-side, right-side, both or
          neither
          """
          return self._data._closed
  
      @Appender(_interval_shared_docs['set_closed'] % _index_doc_kwargs)
      def set_closed(self, closed):
          if closed not in _VALID_CLOSED:
              msg = "invalid option for 'closed': {closed}"
              raise ValueError(msg.format(closed=closed))
  
          # return self._shallow_copy(closed=closed)
          array = self._data.set_closed(closed)
          return self._simple_new(array, self.name)
  
      @property
      def length(self):
          """
          Return an Index with entries denoting the length of each Interval in
          the IntervalIndex
          """
          return self._data.length
  
      @property
      def size(self):
          # Avoid materializing ndarray[Interval]
          return self._data.size
  
      @property
      def shape(self):
          # Avoid materializing ndarray[Interval]
          return self._data.shape
  
      @property
      def itemsize(self):
          msg = ('IntervalIndex.itemsize is deprecated and will be removed in '
                 'a future version')
          warnings.warn(msg, FutureWarning, stacklevel=2)
  
          # supress the warning from the underlying left/right itemsize
          with warnings.catch_warnings():
              warnings.simplefilter('ignore')
              return self.left.itemsize + self.right.itemsize
  
      def __len__(self):
          return len(self.left)
  
      @cache_readonly
      def values(self):
          """
          Return the IntervalIndex's data as an IntervalArray.
          """
          return self._data
  
      @cache_readonly
      def _values(self):
          return self._data
  
      @cache_readonly
      def _ndarray_values(self):
          return np.array(self._data)
  
      def __array__(self, result=None):
          """ the array interface, return my values """
          return self._ndarray_values
  
      def __array_wrap__(self, result, context=None):
          # we don't want the superclass implementation
          return result
  
      def __reduce__(self):
          d = dict(left=self.left,
                   right=self.right)
          d.update(self._get_attributes_dict())
          return _new_IntervalIndex, (self.__class__, d), None
  
      @Appender(_index_shared_docs['copy'])
      def copy(self, deep=False, name=None):
          array = self._data.copy(deep=deep)
          attributes = self._get_attributes_dict()
          if name is not None:
              attributes.update(name=name)
  
          return self._simple_new(array, **attributes)
  
      @Appender(_index_shared_docs['astype'])
      def astype(self, dtype, copy=True):
          with rewrite_exception('IntervalArray', self.__class__.__name__):
              new_values = self.values.astype(dtype, copy=copy)
          if is_interval_dtype(new_values):
              return self._shallow_copy(new_values.left, new_values.right)
          return super().astype(dtype, copy=copy)
  
      @cache_readonly
      def dtype(self):
          """Return the dtype object of the underlying data"""
          return self._data.dtype
  
      @property
      def inferred_type(self):
          """Return a string of the type inferred from the values"""
          return 'interval'
  
      @Appender(Index.memory_usage.__doc__)
      def memory_usage(self, deep=False):
          # we don't use an explicit engine
          # so return the bytes here
          return (self.left.memory_usage(deep=deep) +
                  self.right.memory_usage(deep=deep))
  
      @cache_readonly
      def mid(self):
          """
          Return the midpoint of each Interval in the IntervalIndex as an Index
          """
          return self._data.mid
  
      @cache_readonly
      def is_monotonic(self):
          """
          Return True if the IntervalIndex is monotonic increasing (only equal or
          increasing values), else False
          """
          return self.is_monotonic_increasing
  
      @cache_readonly
      def is_monotonic_increasing(self):
          """
          Return True if the IntervalIndex is monotonic increasing (only equal or
          increasing values), else False
          """
          return self._engine.is_monotonic_increasing
  
      @cache_readonly
      def is_monotonic_decreasing(self):
          """
          Return True if the IntervalIndex is monotonic decreasing (only equal or
          decreasing values), else False
          """
          return self[::-1].is_monotonic_increasing
  
      @cache_readonly
      def is_unique(self):
          """
          Return True if the IntervalIndex contains unique elements, else False
          """
          left = self.left
          right = self.right
  
          if self.isna().sum() > 1:
              return False
  
          if left.is_unique or right.is_unique:
              return True
  
          seen_pairs = set()
          check_idx = np.where(left.duplicated(keep=False))[0]
          for idx in check_idx:
              pair = (left[idx], right[idx])
              if pair in seen_pairs:
                  return False
              seen_pairs.add(pair)
  
          return True
  
      @cache_readonly
      @Appender(_interval_shared_docs['is_non_overlapping_monotonic']
                % _index_doc_kwargs)
      def is_non_overlapping_monotonic(self):
          return self._data.is_non_overlapping_monotonic
  
      @property
      def is_overlapping(self):
          """
          Return True if the IntervalIndex has overlapping intervals, else False.
  
          Two intervals overlap if they share a common point, including closed
          endpoints. Intervals that only have an open endpoint in common do not
          overlap.
  
          .. versionadded:: 0.24.0
  
          Returns
          -------
          bool
              Boolean indicating if the IntervalIndex has overlapping intervals.
  
          See Also
          --------
          Interval.overlaps : Check whether two Interval objects overlap.
          IntervalIndex.overlaps : Check an IntervalIndex elementwise for
              overlaps.
  
          Examples
          --------
          >>> index = pd.IntervalIndex.from_tuples([(0, 2), (1, 3), (4, 5)])
          >>> index
          IntervalIndex([(0, 2], (1, 3], (4, 5]],
                closed='right',
                dtype='interval[int64]')
          >>> index.is_overlapping
          True
  
          Intervals that share closed endpoints overlap:
  
          >>> index = pd.interval_range(0, 3, closed='both')
          >>> index
          IntervalIndex([[0, 1], [1, 2], [2, 3]],
                closed='both',
                dtype='interval[int64]')
          >>> index.is_overlapping
          True
  
          Intervals that only have an open endpoint in common do not overlap:
  
          >>> index = pd.interval_range(0, 3, closed='left')
          >>> index
          IntervalIndex([[0, 1), [1, 2), [2, 3)],
                closed='left',
                dtype='interval[int64]')
          >>> index.is_overlapping
          False
          """
          # GH 23309
          return self._engine.is_overlapping
  
      @Appender(_index_shared_docs['_convert_scalar_indexer'])
      def _convert_scalar_indexer(self, key, kind=None):
          if kind == 'iloc':
              return super()._convert_scalar_indexer(key, kind=kind)
          return key
  
      def _maybe_cast_slice_bound(self, label, side, kind):
          return getattr(self, side)._maybe_cast_slice_bound(label, side, kind)
  
      @Appender(_index_shared_docs['_convert_list_indexer'])
      def _convert_list_indexer(self, keyarr, kind=None):
          """
          we are passed a list-like indexer. Return the
          indexer for matching intervals.
          """
          locs = self.get_indexer_for(keyarr)
  
          # we have missing values
          if (locs == -1).any():
              raise KeyError
  
          return locs
  
      def _maybe_cast_indexed(self, key):
          """
          we need to cast the key, which could be a scalar
          or an array-like to the type of our subtype
          """
          if isinstance(key, IntervalIndex):
              return key
  
          subtype = self.dtype.subtype
          if is_float_dtype(subtype):
              if is_integer(key):
                  key = float(key)
              elif isinstance(key, (np.ndarray, Index)):
                  key = key.astype('float64')
          elif is_integer_dtype(subtype):
              if is_integer(key):
                  key = int(key)
  
          return key
  
      def _needs_i8_conversion(self, key):
          """
          Check if a given key needs i8 conversion. Conversion is necessary for
          Timestamp, Timedelta, DatetimeIndex, and TimedeltaIndex keys. An
          Interval-like requires conversion if it's endpoints are one of the
          aforementioned types.
  
          Assumes that any list-like data has already been cast to an Index.
  
          Parameters
          ----------
          key : scalar or Index-like
              The key that should be checked for i8 conversion
  
          Returns
          -------
          boolean
          """
          if is_interval_dtype(key) or isinstance(key, Interval):
              return self._needs_i8_conversion(key.left)
  
          i8_types = (Timestamp, Timedelta, DatetimeIndex, TimedeltaIndex)
          return isinstance(key, i8_types)
  
      def _maybe_convert_i8(self, key):
          """
          Maybe convert a given key to it's equivalent i8 value(s). Used as a
          preprocessing step prior to IntervalTree queries (self._engine), which
          expects numeric data.
  
          Parameters
          ----------
          key : scalar or list-like
              The key that should maybe be converted to i8.
  
          Returns
          -------
          key: scalar or list-like
              The original key if no conversion occured, int if converted scalar,
              Int64Index if converted list-like.
          """
          original = key
          if is_list_like(key):
              key = ensure_index(key)
  
          if not self._needs_i8_conversion(key):
              return original
  
          scalar = is_scalar(key)
          if is_interval_dtype(key) or isinstance(key, Interval):
              # convert left/right and reconstruct
              left = self._maybe_convert_i8(key.left)
              right = self._maybe_convert_i8(key.right)
              constructor = Interval if scalar else IntervalIndex.from_arrays
              return constructor(left, right, closed=self.closed)
  
          if scalar:
              # Timestamp/Timedelta
              key_dtype, key_i8 = infer_dtype_from_scalar(key, pandas_dtype=True)
          else:
              # DatetimeIndex/TimedeltaIndex
              key_dtype, key_i8 = key.dtype, Index(key.asi8)
              if key.hasnans:
                  # convert NaT from it's i8 value to np.nan so it's not viewed
                  # as a valid value, maybe causing errors (e.g. is_overlapping)
                  key_i8 = key_i8.where(~key._isnan)
  
          # ensure consistency with IntervalIndex subtype
          subtype = self.dtype.subtype
          msg = ('Cannot index an IntervalIndex of subtype {subtype} with '
                 'values of dtype {other}')
          if not is_dtype_equal(subtype, key_dtype):
              raise ValueError(msg.format(subtype=subtype, other=key_dtype))
  
          return key_i8
  
      def _check_method(self, method):
          if method is None:
              return
  
          if method in ['bfill', 'backfill', 'pad', 'ffill', 'nearest']:
              msg = 'method {method} not yet implemented for IntervalIndex'
              raise NotImplementedError(msg.format(method=method))
  
          raise ValueError("Invalid fill method")
  
      def _searchsorted_monotonic(self, label, side, exclude_label=False):
          if not self.is_non_overlapping_monotonic:
              raise KeyError('can only get slices from an IntervalIndex if '
                             'bounds are non-overlapping and all monotonic '
                             'increasing or decreasing')
  
          if isinstance(label, IntervalMixin):
              raise NotImplementedError
  
          # GH 20921: "not is_monotonic_increasing" for the second condition
          # instead of "is_monotonic_decreasing" to account for single element
          # indexes being both increasing and decreasing
          if ((side == 'left' and self.left.is_monotonic_increasing) or
                  (side == 'right' and not self.left.is_monotonic_increasing)):
              sub_idx = self.right
              if self.open_right or exclude_label:
                  label = _get_next_label(label)
          else:
              sub_idx = self.left
              if self.open_left or exclude_label:
                  label = _get_prev_label(label)
  
          return sub_idx._searchsorted_monotonic(label, side)
  
      def _get_loc_only_exact_matches(self, key):
          if isinstance(key, Interval):
  
              if not self.is_unique:
                  raise ValueError("cannot index with a slice Interval"
                                   " and a non-unique index")
  
              # TODO: this expands to a tuple index, see if we can
              # do better
              return Index(self._multiindex.values).get_loc(key)
          raise KeyError
  
      def _find_non_overlapping_monotonic_bounds(self, key):
          if isinstance(key, IntervalMixin):
              start = self._searchsorted_monotonic(
                  key.left, 'left', exclude_label=key.open_left)
              stop = self._searchsorted_monotonic(
                  key.right, 'right', exclude_label=key.open_right)
          elif isinstance(key, slice):
              # slice
              start, stop = key.start, key.stop
              if (key.step or 1) != 1:
                  raise NotImplementedError("cannot slice with a slice step")
              if start is None:
                  start = 0
              else:
                  start = self._searchsorted_monotonic(start, 'left')
              if stop is None:
                  stop = len(self)
              else:
                  stop = self._searchsorted_monotonic(stop, 'right')
          else:
              # scalar or index-like
  
              start = self._searchsorted_monotonic(key, 'left')
              stop = self._searchsorted_monotonic(key, 'right')
          return start, stop
  
      def get_loc(self, key, method=None):
          """
          Get integer location, slice or boolean mask for requested label.
  
          Parameters
          ----------
          key : label
          method : {None}, optional
              * default: matches where the label is within an interval only.
  
          Returns
          -------
          loc : int if unique index, slice if monotonic index, else mask
  
          Examples
          --------
          >>> i1, i2 = pd.Interval(0, 1), pd.Interval(1, 2)
          >>> index = pd.IntervalIndex([i1, i2])
          >>> index.get_loc(1)
          0
  
          You can also supply an interval or an location for a point inside an
          interval.
  
          >>> index.get_loc(pd.Interval(0, 2))
          array([0, 1], dtype=int64)
          >>> index.get_loc(1.5)
          1
  
          If a label is in several intervals, you get the locations of all the
          relevant intervals.
  
          >>> i3 = pd.Interval(0, 2)
          >>> overlapping_index = pd.IntervalIndex([i2, i3])
          >>> overlapping_index.get_loc(1.5)
          array([0, 1], dtype=int64)
          """
          self._check_method(method)
  
          original_key = key
          key = self._maybe_cast_indexed(key)
  
          if self.is_non_overlapping_monotonic:
              if isinstance(key, Interval):
                  left = self._maybe_cast_slice_bound(key.left, 'left', None)
                  right = self._maybe_cast_slice_bound(key.right, 'right', None)
                  key = Interval(left, right, key.closed)
              else:
                  key = self._maybe_cast_slice_bound(key, 'left', None)
  
              start, stop = self._find_non_overlapping_monotonic_bounds(key)
  
              if start is None or stop is None:
                  return slice(start, stop)
              elif start + 1 == stop:
                  return start
              elif start < stop:
                  return slice(start, stop)
              else:
                  raise KeyError(original_key)
  
          else:
              # use the interval tree
              key = self._maybe_convert_i8(key)
              if isinstance(key, Interval):
                  left, right = _get_interval_closed_bounds(key)
                  return self._engine.get_loc_interval(left, right)
              else:
                  return self._engine.get_loc(key)
  
      def get_value(self, series, key):
          if com.is_bool_indexer(key):
              loc = key
          elif is_list_like(key):
              loc = self.get_indexer(key)
          elif isinstance(key, slice):
  
              if not (key.step is None or key.step == 1):
                  raise ValueError("cannot support not-default step in a slice")
  
              try:
                  loc = self.get_loc(key)
              except TypeError:
                  # we didn't find exact intervals or are non-unique
                  msg = "unable to slice with this key: {key}".format(key=key)
                  raise ValueError(msg)
  
          else:
              loc = self.get_loc(key)
          return series.iloc[loc]
  
      @Substitution(**dict(_index_doc_kwargs,
                           **{'raises_section': textwrap.dedent("""
          Raises
          ------
          NotImplementedError
              If any method argument other than the default of
              None is specified as these are not yet implemented.
          """)}))
      @Appender(_index_shared_docs['get_indexer'])
      def get_indexer(self, target, method=None, limit=None, tolerance=None):
  
          self._check_method(method)
          target = ensure_index(target)
          target = self._maybe_cast_indexed(target)
  
          if self.equals(target):
              return np.arange(len(self), dtype='intp')
  
          if self.is_non_overlapping_monotonic:
              start, stop = self._find_non_overlapping_monotonic_bounds(target)
  
              start_plus_one = start + 1
              if not ((start_plus_one < stop).any()):
                  return np.where(start_plus_one == stop, start, -1)
  
          if not self.is_unique:
              raise ValueError("cannot handle non-unique indices")
  
          # IntervalIndex
          if isinstance(target, IntervalIndex):
              indexer = self._get_reindexer(target)
  
          # non IntervalIndex
          else:
              indexer = np.concatenate([self.get_loc(i) for i in target])
  
          return ensure_platform_int(indexer)
  
      def _get_reindexer(self, target):
          """
          Return an indexer for a target IntervalIndex with self
          """
  
          # find the left and right indexers
          left = self._maybe_convert_i8(target.left)
          right = self._maybe_convert_i8(target.right)
          lindexer = self._engine.get_indexer(left.values)
          rindexer = self._engine.get_indexer(right.values)
  
          # we want to return an indexer on the intervals
          # however, our keys could provide overlapping of multiple
          # intervals, so we iterate thru the indexers and construct
          # a set of indexers
  
          indexer = []
          n = len(self)
  
          for i, (lhs, rhs) in enumerate(zip(lindexer, rindexer)):
  
              target_value = target[i]
  
              # matching on the lhs bound
              if (lhs != -1 and
                      self.closed == 'right' and
                      target_value.left == self[lhs].right):
                  lhs += 1
  
              # matching on the lhs bound
              if (rhs != -1 and
                      self.closed == 'left' and
                      target_value.right == self[rhs].left):
                  rhs -= 1
  
              # not found
              if lhs == -1 and rhs == -1:
                  indexer.append(np.array([-1]))
  
              elif rhs == -1:
  
                  indexer.append(np.arange(lhs, n))
  
              elif lhs == -1:
  
                  # care about left/right closed here
                  value = self[i]
  
                  # target.closed same as self.closed
                  if self.closed == target.closed:
                      if target_value.left < value.left:
                          indexer.append(np.array([-1]))
                          continue
  
                  # target.closed == 'left'
                  elif self.closed == 'right':
                      if target_value.left <= value.left:
                          indexer.append(np.array([-1]))
                          continue
  
                  # target.closed == 'right'
                  elif self.closed == 'left':
                      if target_value.left <= value.left:
                          indexer.append(np.array([-1]))
                          continue
  
                  indexer.append(np.arange(0, rhs + 1))
  
              else:
                  indexer.append(np.arange(lhs, rhs + 1))
  
          return np.concatenate(indexer)
  
      @Appender(_index_shared_docs['get_indexer_non_unique'] % _index_doc_kwargs)
      def get_indexer_non_unique(self, target):
          target = self._maybe_cast_indexed(ensure_index(target))
          return super().get_indexer_non_unique(target)
  
      @Appender(_index_shared_docs['where'])
      def where(self, cond, other=None):
          if other is None:
              other = self._na_value
          values = np.where(cond, self.values, other)
          return self._shallow_copy(values)
  
      def delete(self, loc):
          """
          Return a new IntervalIndex with passed location(-s) deleted
  
          Returns
          -------
          new_index : IntervalIndex
          """
          new_left = self.left.delete(loc)
          new_right = self.right.delete(loc)
          return self._shallow_copy(new_left, new_right)
  
      def insert(self, loc, item):
          """
          Return a new IntervalIndex inserting new item at location. Follows
          Python list.append semantics for negative values.  Only Interval
          objects and NA can be inserted into an IntervalIndex
  
          Parameters
          ----------
          loc : int
          item : object
  
          Returns
          -------
          new_index : IntervalIndex
          """
          if isinstance(item, Interval):
              if item.closed != self.closed:
                  raise ValueError('inserted item must be closed on the same '
                                   'side as the index')
              left_insert = item.left
              right_insert = item.right
          elif is_scalar(item) and isna(item):
              # GH 18295
              left_insert = right_insert = item
          else:
              raise ValueError('can only insert Interval objects and NA into '
                               'an IntervalIndex')
  
          new_left = self.left.insert(loc, left_insert)
          new_right = self.right.insert(loc, right_insert)
          return self._shallow_copy(new_left, new_right)
  
      def _concat_same_dtype(self, to_concat, name):
          """
          assert that we all have the same .closed
          we allow a 0-len index here as well
          """
          if not len({i.closed for i in to_concat if len(i)}) == 1:
              msg = ('can only append two IntervalIndex objects '
                     'that are closed on the same side')
              raise ValueError(msg)
          return super()._concat_same_dtype(to_concat, name)
  
      @Appender(_index_shared_docs['take'] % _index_doc_kwargs)
      def take(self, indices, axis=0, allow_fill=True,
               fill_value=None, **kwargs):
          result = self._data.take(indices, axis=axis, allow_fill=allow_fill,
                                   fill_value=fill_value, **kwargs)
          attributes = self._get_attributes_dict()
          return self._simple_new(result, **attributes)
  
      def __getitem__(self, value):
          result = self._data[value]
          if isinstance(result, IntervalArray):
              return self._shallow_copy(result)
          else:
              # scalar
              return result
  
      # --------------------------------------------------------------------
      # Rendering Methods
      # __repr__ associated methods are based on MultiIndex
  
      def _format_with_header(self, header, **kwargs):
          return header + list(self._format_native_types(**kwargs))
  
      def _format_native_types(self, na_rep='NaN', quoting=None, **kwargs):
          """ actually format my specific types """
          from pandas.io.formats.format import ExtensionArrayFormatter
          return ExtensionArrayFormatter(values=self,
                                         na_rep=na_rep,
                                         justify='all',
                                         leading_space=False).get_result()
  
      def _format_data(self, name=None):
  
          # TODO: integrate with categorical and make generic
          # name argument is unused here; just for compat with base / categorical
          n = len(self)
          max_seq_items = min((get_option(
              'display.max_seq_items') or n) // 10, 10)
  
          formatter = str
  
          if n == 0:
              summary = '[]'
          elif n == 1:
              first = formatter(self[0])
              summary = '[{first}]'.format(first=first)
          elif n == 2:
              first = formatter(self[0])
              last = formatter(self[-1])
              summary = '[{first}, {last}]'.format(first=first, last=last)
          else:
  
              if n > max_seq_items:
                  n = min(max_seq_items // 2, 10)
                  head = [formatter(x) for x in self[:n]]
                  tail = [formatter(x) for x in self[-n:]]
                  summary = '[{head} ... {tail}]'.format(
                      head=', '.join(head), tail=', '.join(tail))
              else:
                  tail = [formatter(x) for x in self]
                  summary = '[{tail}]'.format(tail=', '.join(tail))
  
          return summary + ',' + self._format_space()
  
      def _format_attrs(self):
          attrs = [('closed', repr(self.closed))]
          if self.name is not None:
              attrs.append(('name', default_pprint(self.name)))
          attrs.append(('dtype', "'{dtype}'".format(dtype=self.dtype)))
          return attrs
  
      def _format_space(self):
          space = ' ' * (len(self.__class__.__name__) + 1)
          return "\n{space}".format(space=space)
  
      # --------------------------------------------------------------------
  
      def argsort(self, *args, **kwargs):
          return np.lexsort((self.right, self.left))
  
      def equals(self, other):
          """
          Determines if two IntervalIndex objects contain the same elements
          """
          if self.is_(other):
              return True
  
          # if we can coerce to an II
          # then we can compare
          if not isinstance(other, IntervalIndex):
              if not is_interval_dtype(other):
                  return False
              other = Index(getattr(other, '.values', other))
  
          return (self.left.equals(other.left) and
                  self.right.equals(other.right) and
                  self.closed == other.closed)
  
      @Appender(_interval_shared_docs['overlaps'] % _index_doc_kwargs)
      def overlaps(self, other):
          return self._data.overlaps(other)
  
      @Appender(_index_shared_docs['intersection'])
      @SetopCheck(op_name='intersection')
      def intersection(self,
                       other: 'IntervalIndex',
                       sort: bool = False
                       ) -> 'IntervalIndex':
          if self.left.is_unique and self.right.is_unique:
              taken = self._intersection_unique(other)
          elif (other.left.is_unique and other.right.is_unique and
                self.isna().sum() <= 1):
              # Swap other/self if other is unique and self does not have
              # multiple NaNs
              taken = other._intersection_unique(self)
          else:
              # duplicates
              taken = self._intersection_non_unique(other)
  
          if sort is None:
              taken = taken.sort_values()
  
          return taken
  
      def _intersection_unique(self,
                               other: 'IntervalIndex'
                               ) -> 'IntervalIndex':
          """
          Used when the IntervalIndex does not have any common endpoint,
          no mater left or right.
          Return the intersection with another IntervalIndex.
  
          Parameters
          ----------
          other : IntervalIndex
  
          Returns
          -------
          taken : IntervalIndex
          """
          lindexer = self.left.get_indexer(other.left)
          rindexer = self.right.get_indexer(other.right)
  
          match = (lindexer == rindexer) & (lindexer != -1)
          indexer = lindexer.take(match.nonzero()[0])
  
          return self.take(indexer)
  
      def _intersection_non_unique(self,
                                   other: 'IntervalIndex'
                                   ) -> 'IntervalIndex':
          """
          Used when the IntervalIndex does have some common endpoints,
          on either sides.
          Return the intersection with another IntervalIndex.
  
          Parameters
          ----------
          other : IntervalIndex
  
          Returns
          -------
          taken : IntervalIndex
          """
          mask = np.zeros(len(self), dtype=bool)
  
          if self.hasnans and other.hasnans:
              first_nan_loc = np.arange(len(self))[self.isna()][0]
              mask[first_nan_loc] = True
  
          lmiss = other.left.get_indexer_non_unique(self.left)[1]
          lmatch = np.setdiff1d(np.arange(len(self)), lmiss)
  
          for i in lmatch:
              potential = other.left.get_loc(self.left[i])
              if is_scalar(potential):
                  if self.right[i] == other.right[potential]:
                      mask[i] = True
              elif self.right[i] in other.right[potential]:
                  mask[i] = True
  
          return self[mask]
  
      def _setop(op_name, sort=None):
          @SetopCheck(op_name=op_name)
          def func(self, other, sort=sort):
              result = getattr(self._multiindex, op_name)(other._multiindex,
                                                          sort=sort)
              result_name = get_op_result_name(self, other)
  
              # GH 19101: ensure empty results have correct dtype
              if result.empty:
                  result = result.values.astype(self.dtype.subtype)
              else:
                  result = result.values
  
              return type(self).from_tuples(result, closed=self.closed,
                                            name=result_name)
  
          return func
  
      @property
      def is_all_dates(self):
          """
          This is False even when left/right contain datetime-like objects,
          as the check is done on the Interval itself
          """
          return False
  
      union = _setop('union')
      difference = _setop('difference')
      symmetric_difference = _setop('symmetric_difference')
  
      # TODO: arithmetic operations
  
  
  IntervalIndex._add_logical_methods_disabled()
  
  
  def _is_valid_endpoint(endpoint):
      """helper for interval_range to check if start/end are valid types"""
      return any([is_number(endpoint),
                  isinstance(endpoint, Timestamp),
                  isinstance(endpoint, Timedelta),
                  endpoint is None])
  
  
  def _is_type_compatible(a, b):
      """helper for interval_range to check type compat of start/end/freq"""
      is_ts_compat = lambda x: isinstance(x, (Timestamp, DateOffset))
      is_td_compat = lambda x: isinstance(x, (Timedelta, DateOffset))
      return ((is_number(a) and is_number(b)) or
              (is_ts_compat(a) and is_ts_compat(b)) or
              (is_td_compat(a) and is_td_compat(b)) or
              com._any_none(a, b))
  
  
  def interval_range(start=None, end=None, periods=None, freq=None,
                     name=None, closed='right'):
      """
      Return a fixed frequency IntervalIndex
  
      Parameters
      ----------
      start : numeric or datetime-like, default None
          Left bound for generating intervals
      end : numeric or datetime-like, default None
          Right bound for generating intervals
      periods : integer, default None
          Number of periods to generate
      freq : numeric, string, or DateOffset, default None
          The length of each interval. Must be consistent with the type of start
          and end, e.g. 2 for numeric, or '5H' for datetime-like.  Default is 1
          for numeric and 'D' for datetime-like.
      name : string, default None
          Name of the resulting IntervalIndex
      closed : {'left', 'right', 'both', 'neither'}, default 'right'
          Whether the intervals are closed on the left-side, right-side, both
          or neither.
  
      Returns
      -------
      rng : IntervalIndex
  
      See Also
      --------
      IntervalIndex : An Index of intervals that are all closed on the same side.
  
      Notes
      -----
      Of the four parameters ``start``, ``end``, ``periods``, and ``freq``,
      exactly three must be specified. If ``freq`` is omitted, the resulting
      ``IntervalIndex`` will have ``periods`` linearly spaced elements between
      ``start`` and ``end``, inclusively.
  
      To learn more about datetime-like frequency strings, please see `this link
      <http://pandas.pydata.org/pandas-docs/stable/user_guide/timeseries.html#offset-aliases>`__.
  
      Examples
      --------
      Numeric ``start`` and  ``end`` is supported.
  
      >>> pd.interval_range(start=0, end=5)
      IntervalIndex([(0, 1], (1, 2], (2, 3], (3, 4], (4, 5]],
                    closed='right', dtype='interval[int64]')
  
      Additionally, datetime-like input is also supported.
  
      >>> pd.interval_range(start=pd.Timestamp('2017-01-01'),
      ...                   end=pd.Timestamp('2017-01-04'))
      IntervalIndex([(2017-01-01, 2017-01-02], (2017-01-02, 2017-01-03],
                     (2017-01-03, 2017-01-04]],
                    closed='right', dtype='interval[datetime64[ns]]')
  
      The ``freq`` parameter specifies the frequency between the left and right.
      endpoints of the individual intervals within the ``IntervalIndex``.  For
      numeric ``start`` and ``end``, the frequency must also be numeric.
  
      >>> pd.interval_range(start=0, periods=4, freq=1.5)
      IntervalIndex([(0.0, 1.5], (1.5, 3.0], (3.0, 4.5], (4.5, 6.0]],
                    closed='right', dtype='interval[float64]')
  
      Similarly, for datetime-like ``start`` and ``end``, the frequency must be
      convertible to a DateOffset.
  
      >>> pd.interval_range(start=pd.Timestamp('2017-01-01'),
      ...                   periods=3, freq='MS')
      IntervalIndex([(2017-01-01, 2017-02-01], (2017-02-01, 2017-03-01],
                     (2017-03-01, 2017-04-01]],
                    closed='right', dtype='interval[datetime64[ns]]')
  
      Specify ``start``, ``end``, and ``periods``; the frequency is generated
      automatically (linearly spaced).
  
      >>> pd.interval_range(start=0, end=6, periods=4)
      IntervalIndex([(0.0, 1.5], (1.5, 3.0], (3.0, 4.5], (4.5, 6.0]],
                closed='right',
                dtype='interval[float64]')
  
      The ``closed`` parameter specifies which endpoints of the individual
      intervals within the ``IntervalIndex`` are closed.
  
      >>> pd.interval_range(end=5, periods=4, closed='both')
      IntervalIndex([[1, 2], [2, 3], [3, 4], [4, 5]],
                    closed='both', dtype='interval[int64]')
      """
      start = com.maybe_box_datetimelike(start)
      end = com.maybe_box_datetimelike(end)
      endpoint = start if start is not None else end
  
      if freq is None and com._any_none(periods, start, end):
          freq = 1 if is_number(endpoint) else 'D'
  
      if com.count_not_none(start, end, periods, freq) != 3:
          raise ValueError('Of the four parameters: start, end, periods, and '
                           'freq, exactly three must be specified')
  
      if not _is_valid_endpoint(start):
          msg = 'start must be numeric or datetime-like, got {start}'
          raise ValueError(msg.format(start=start))
      elif not _is_valid_endpoint(end):
          msg = 'end must be numeric or datetime-like, got {end}'
          raise ValueError(msg.format(end=end))
  
      if is_float(periods):
          periods = int(periods)
      elif not is_integer(periods) and periods is not None:
          msg = 'periods must be a number, got {periods}'
          raise TypeError(msg.format(periods=periods))
  
      if freq is not None and not is_number(freq):
          try:
              freq = to_offset(freq)
          except ValueError:
              raise ValueError('freq must be numeric or convertible to '
                               'DateOffset, got {freq}'.format(freq=freq))
  
      # verify type compatibility
      if not all([_is_type_compatible(start, end),
                  _is_type_compatible(start, freq),
                  _is_type_compatible(end, freq)]):
          raise TypeError("start, end, freq need to be type compatible")
  
      # +1 to convert interval count to breaks count (n breaks = n-1 intervals)
      if periods is not None:
          periods += 1
  
      if is_number(endpoint):
          # force consistency between start/end/freq (lower end if freq skips it)
          if com._all_not_none(start, end, freq):
              end -= (end - start) % freq
  
          # compute the period/start/end if unspecified (at most one)
          if periods is None:
              periods = int((end - start) // freq) + 1
          elif start is None:
              start = end - (periods - 1) * freq
          elif end is None:
              end = start + (periods - 1) * freq
  
          breaks = np.linspace(start, end, periods)
          if all(is_integer(x) for x in com._not_none(start, end, freq)):
              # np.linspace always produces float output
              breaks = maybe_downcast_to_dtype(breaks, 'int64')
      else:
          # delegate to the appropriate range function
          if isinstance(endpoint, Timestamp):
              range_func = date_range
          else:
              range_func = timedelta_range
  
          breaks = range_func(start=start, end=end, periods=periods, freq=freq)
  
      return IntervalIndex.from_breaks(breaks, name=name, closed=closed)
  