text: """ define the IntervalIndex """
  from operator import le, lt
  import textwrap
  from typing import Any, Optional, Tuple, Union
  
  import numpy as np
  
  from pandas._config import get_option
  
  from pandas._libs import lib
  from pandas._libs.interval import Interval, IntervalMixin, IntervalTree
  from pandas._libs.tslibs import Timedelta, Timestamp, to_offset
  from pandas._typing import AnyArrayLike, Label
  from pandas.errors import InvalidIndexError
  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_categorical_dtype,
      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.algorithms import take_1d
  from pandas.core.arrays.interval import IntervalArray, _interval_shared_docs
  import pandas.core.common as com
  from pandas.core.indexers import is_valid_positional_slice
  import pandas.core.indexes.base as ibase
  from pandas.core.indexes.base import (
      Index,
      _index_shared_docs,
      default_pprint,
      ensure_index,
      maybe_extract_name,
  )
  from pandas.core.indexes.datetimes import DatetimeIndex, date_range
  from pandas.core.indexes.extension import ExtensionIndex, inherit_names
  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.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(f"cannot determine next label for type {repr(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(f"cannot determine next label for type {repr(type(label))}")
  
  
  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:
                  raise ValueError(
                      "can only do set operations between two IntervalIndex "
                      "objects that are closed on the same side"
                  )
  
              # 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):
                  raise TypeError(
                      f"can only do {self.op_name} between two IntervalIndex "
                      "objects that have compatible dtypes"
                  )
  
              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="",
          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.
      """
          ),
      )
  )
  @inherit_names(["set_closed", "to_tuples"], IntervalArray, wrap=True)
  @inherit_names(
      ["__array__", "overlaps", "contains", "left", "right", "length"], IntervalArray,
  )
  @inherit_names(
      ["is_non_overlapping_monotonic", "mid", "closed"], IntervalArray, cache=True,
  )
  class IntervalIndex(IntervalMixin, ExtensionIndex):
      _typ = "intervalindex"
      _comparables = ["name"]
      _attributes = ["name"]
  
      # 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
  
      _data: IntervalArray
      # --------------------------------------------------------------------
      # Constructors
  
      def __new__(
          cls,
          data,
          closed=None,
          dtype=None,
          copy: bool = False,
          name=None,
          verify_integrity: bool = True,
      ):
  
          name = maybe_extract_name(name, data, cls)
  
          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: IntervalArray, name: Label = None):
          """
          Construct from an IntervalArray
  
          Parameters
          ----------
          array : IntervalArray
          name : Label, default None
              Attached as result.name
          """
          assert isinstance(array, IntervalArray), type(array)
  
          result = IntervalMixin.__new__(cls)
          result._data = array
          result.name = name
          result._cache = {}
          result._no_setting_name = False
          result._reset_identity()
          return result
  
      @classmethod
      @Appender(
          _interval_shared_docs["from_breaks"]
          % dict(
              klass="IntervalIndex",
              examples=textwrap.dedent(
                  """\
          Examples
          --------
          >>> pd.IntervalIndex.from_breaks([0, 1, 2, 3])
          IntervalIndex([(0, 1], (1, 2], (2, 3]],
                        closed='right',
                        dtype='interval[int64]')
          """
              ),
          )
      )
      def from_breaks(
          cls, breaks, closed: str = "right", name=None, copy: bool = 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"]
          % dict(
              klass="IntervalIndex",
              examples=textwrap.dedent(
                  """\
          Examples
          --------
          >>> pd.IntervalIndex.from_arrays([0, 1, 2], [1, 2, 3])
          IntervalIndex([(0, 1], (1, 2], (2, 3]],
                        closed='right',
                        dtype='interval[int64]')
          """
              ),
          )
      )
      def from_arrays(
          cls,
          left,
          right,
          closed: str = "right",
          name=None,
          copy: bool = 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_tuples"]
          % dict(
              klass="IntervalIndex",
              examples=textwrap.dedent(
                  """\
          Examples
          --------
          >>> pd.IntervalIndex.from_tuples([(0, 1), (1, 2)])
          IntervalIndex([(0, 1], (1, 2]],
                         closed='right',
                         dtype='interval[int64]')
          """
              ),
          )
      )
      def from_tuples(
          cls, data, closed: str = "right", name=None, copy: bool = 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._shallow_copy.__doc__)
      def _shallow_copy(self, values=None, name: Label = lib.no_default):
          name = self.name if name is lib.no_default else name
          cache = self._cache.copy() if values is None else {}
          if values is None:
              values = self._data
  
          result = self._simple_new(values, name=name)
          result._cache = cache
          return result
  
      @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: Any) -> bool:
          """
          return a boolean if this key is IN the index
          We *only* accept an Interval
  
          Parameters
          ----------
          key : Interval
  
          Returns
          -------
          bool
          """
          hash(key)
          if not isinstance(key, Interval):
              return False
  
          try:
              self.get_loc(key)
              return True
          except KeyError:
              return False
  
      @cache_readonly
      def _multiindex(self) -> MultiIndex:
          return MultiIndex.from_arrays([self.left, self.right], names=["left", "right"])
  
      @cache_readonly
      def values(self) -> IntervalArray:
          """
          Return the IntervalIndex's data as an IntervalArray.
          """
          return self._data
  
      @property
      def _has_complex_internals(self) -> bool:
          # used to avoid libreduction code paths, which raise or require conversion
          return True
  
      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, (type(self), d), None
  
      @Appender(Index.astype.__doc__)
      def astype(self, dtype, copy=True):
          with rewrite_exception("IntervalArray", type(self).__name__):
              new_values = self._values.astype(dtype, copy=copy)
          if is_interval_dtype(new_values.dtype):
              return self._shallow_copy(new_values)
          return Index.astype(self, dtype, copy=copy)
  
      @property
      def inferred_type(self) -> str:
          """Return a string of the type inferred from the values"""
          return "interval"
  
      @Appender(Index.memory_usage.__doc__)
      def memory_usage(self, deep: bool = False) -> int:
          # 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)
  
      # IntervalTree doesn't have a is_monotonic_decreasing, so have to override
      #  the Index implementation
      @cache_readonly
      def is_monotonic_decreasing(self) -> bool:
          """
          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
  
      @property
      def is_overlapping(self) -> bool:
          """
          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
  
      def _should_fallback_to_positional(self) -> bool:
          # integer lookups in Series.__getitem__ are unambiguously
          #  positional in this case
          return self.dtype.subtype.kind in ["m", "M"]
  
      def _maybe_cast_slice_bound(self, label, side, kind):
          return getattr(self, side)._maybe_cast_slice_bound(label, side, kind)
  
      @Appender(Index._convert_list_indexer.__doc__)
      def _convert_list_indexer(self, keyarr):
          """
          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 _can_reindex(self, indexer: np.ndarray) -> None:
          """
          Check if we are allowing reindexing with this particular indexer.
  
          Parameters
          ----------
          indexer : an integer indexer
  
          Raises
          ------
          ValueError if its a duplicate axis
          """
          # trying to reindex on an axis with duplicates
          if self.is_overlapping and len(indexer):
              raise ValueError("cannot reindex from an overlapping axis")
  
      def _needs_i8_conversion(self, key) -> bool:
          """
          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
          -------
          bool
          """
          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
          -------
          scalar or list-like
              The original key if no conversion occurred, 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
  
          if not is_dtype_equal(subtype, key_dtype):
              raise ValueError(
                  f"Cannot index an IntervalIndex of subtype {subtype} with "
                  f"values of dtype {key_dtype}"
              )
  
          return key_i8
  
      def _check_method(self, method):
          if method is None:
              return
  
          if method in ["bfill", "backfill", "pad", "ffill", "nearest"]:
              raise NotImplementedError(
                  f"method {method} not yet implemented for IntervalIndex"
              )
  
          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("Interval objects are not currently supported")
  
          # 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(
          self, key, method: Optional[str] = None, tolerance=None
      ) -> Union[int, slice, np.ndarray]:
          """
          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
          -------
          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 a point inside an interval.
  
          >>> 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([i1, i2, i3])
          >>> overlapping_index.get_loc(0.5)
          array([ True, False,  True])
  
          Only exact matches will be returned if an interval is provided.
  
          >>> index.get_loc(pd.Interval(0, 1))
          0
          """
          self._check_method(method)
  
          if not is_scalar(key):
              raise InvalidIndexError(key)
  
          if isinstance(key, Interval):
              if self.closed != key.closed:
                  raise KeyError(key)
              mask = (self.left == key.left) & (self.right == key.right)
          else:
              # assume scalar
              op_left = le if self.closed_left else lt
              op_right = le if self.closed_right else lt
              try:
                  mask = op_left(self.left, key) & op_right(key, self.right)
              except TypeError as err:
                  # scalar is not comparable to II subtype --> invalid label
                  raise KeyError(key) from err
  
          matches = mask.sum()
          if matches == 0:
              raise KeyError(key)
          elif matches == 1:
              return mask.argmax()
          return lib.maybe_booleans_to_slice(mask.view("u1"))
  
      @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: AnyArrayLike,
          method: Optional[str] = None,
          limit: Optional[int] = None,
          tolerance: Optional[Any] = None,
      ) -> np.ndarray:
  
          self._check_method(method)
  
          if self.is_overlapping:
              raise InvalidIndexError(
                  "cannot handle overlapping indices; "
                  "use IntervalIndex.get_indexer_non_unique"
              )
  
          target_as_index = ensure_index(target)
  
          if isinstance(target_as_index, IntervalIndex):
              # equal indexes -> 1:1 positional match
              if self.equals(target_as_index):
                  return np.arange(len(self), dtype="intp")
  
              # different closed or incompatible subtype -> no matches
              common_subtype = find_common_type(
                  [self.dtype.subtype, target_as_index.dtype.subtype]
              )
              if self.closed != target_as_index.closed or is_object_dtype(common_subtype):
                  return np.repeat(np.intp(-1), len(target_as_index))
  
              # non-overlapping -> at most one match per interval in target_as_index
              # want exact matches -> need both left/right to match, so defer to
              # left/right get_indexer, compare elementwise, equality -> match
              left_indexer = self.left.get_indexer(target_as_index.left)
              right_indexer = self.right.get_indexer(target_as_index.right)
              indexer = np.where(left_indexer == right_indexer, left_indexer, -1)
          elif is_categorical_dtype(target_as_index.dtype):
              # get an indexer for unique categories then propagate to codes via take_1d
              categories_indexer = self.get_indexer(target_as_index.categories)
              indexer = take_1d(categories_indexer, target_as_index.codes, fill_value=-1)
          elif not is_object_dtype(target_as_index):
              # homogeneous scalar index: use IntervalTree
              target_as_index = self._maybe_convert_i8(target_as_index)
              indexer = self._engine.get_indexer(target_as_index.values)
          else:
              # heterogeneous scalar index: defer elementwise to get_loc
              # (non-overlapping so get_loc guarantees scalar of KeyError)
              indexer = []
              for key in target_as_index:
                  try:
                      loc = self.get_loc(key)
                  except KeyError:
                      loc = -1
                  except InvalidIndexError as err:
                      # i.e. non-scalar key
                      raise TypeError(key) from err
                  indexer.append(loc)
  
          return ensure_platform_int(indexer)
  
      @Appender(_index_shared_docs["get_indexer_non_unique"] % _index_doc_kwargs)
      def get_indexer_non_unique(
          self, target: AnyArrayLike
      ) -> Tuple[np.ndarray, np.ndarray]:
          target_as_index = ensure_index(target)
  
          # check that target_as_index IntervalIndex is compatible
          if isinstance(target_as_index, IntervalIndex):
              common_subtype = find_common_type(
                  [self.dtype.subtype, target_as_index.dtype.subtype]
              )
              if self.closed != target_as_index.closed or is_object_dtype(common_subtype):
                  # different closed or incompatible subtype -> no matches
                  return (
                      np.repeat(-1, len(target_as_index)),
                      np.arange(len(target_as_index)),
                  )
  
          if is_object_dtype(target_as_index) or isinstance(
              target_as_index, IntervalIndex
          ):
              # target_as_index might contain intervals: defer elementwise to get_loc
              indexer, missing = [], []
              for i, key in enumerate(target_as_index):
                  try:
                      locs = self.get_loc(key)
                      if isinstance(locs, slice):
                          locs = np.arange(locs.start, locs.stop, locs.step, dtype="intp")
                      locs = np.array(locs, ndmin=1)
                  except KeyError:
                      missing.append(i)
                      locs = np.array([-1])
                  indexer.append(locs)
              indexer = np.concatenate(indexer)
          else:
              target_as_index = self._maybe_convert_i8(target_as_index)
              indexer, missing = self._engine.get_indexer_non_unique(
                  target_as_index.values
              )
  
          return ensure_platform_int(indexer), ensure_platform_int(missing)
  
      def get_indexer_for(self, target: AnyArrayLike, **kwargs) -> np.ndarray:
          """
          Guaranteed return of an indexer even when overlapping.
  
          This dispatches to get_indexer or get_indexer_non_unique
          as appropriate.
  
          Returns
          -------
          numpy.ndarray
              List of indices.
          """
          if self.is_overlapping:
              return self.get_indexer_non_unique(target)[0]
          return self.get_indexer(target, **kwargs)
  
      def _convert_slice_indexer(self, key: slice, kind: str):
          if not (key.step is None or key.step == 1):
              # GH#31658 if label-based, we require step == 1,
              #  if positional, we disallow float start/stop
              msg = "label-based slicing with step!=1 is not supported for IntervalIndex"
              if kind == "loc":
                  raise ValueError(msg)
              elif kind == "getitem":
                  if not is_valid_positional_slice(key):
                      # i.e. this cannot be interpreted as a positional slice
                      raise ValueError(msg)
  
          return super()._convert_slice_indexer(key, kind)
  
      @Appender(Index.where.__doc__)
      def where(self, cond, other=None):
          if other is None:
              other = self._na_value
          values = np.where(cond, self._values, other)
          result = IntervalArray(values)
          return self._shallow_copy(result)
  
      def delete(self, loc):
          """
          Return a new IntervalIndex with passed location(-s) deleted
  
          Returns
          -------
          IntervalIndex
          """
          new_left = self.left.delete(loc)
          new_right = self.right.delete(loc)
          result = self._data._shallow_copy(new_left, new_right)
          return self._shallow_copy(result)
  
      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
          -------
          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)
          result = self._data._shallow_copy(new_left, new_right)
          return self._shallow_copy(result)
  
      @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
          )
          return self._shallow_copy(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):
          # GH 28210: use base method but with different default na_rep
          return super()._format_native_types(na_rep=na_rep, quoting=quoting, **kwargs)
  
      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 = f"[{first}]"
          elif n == 2:
              first = formatter(self[0])
              last = formatter(self[-1])
              summary = f"[{first}, {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:]]
                  head_joined = ", ".join(head)
                  tail_joined = ", ".join(tail)
                  summary = f"[{head_joined} ... {tail_joined}]"
              else:
                  tail = [formatter(x) for x in self]
                  joined = ", ".join(tail)
                  summary = f"[{joined}]"
  
          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", f"'{self.dtype}'"))
          return attrs
  
      def _format_space(self) -> str:
          space = " " * (len(type(self).__name__) + 1)
          return f"\n{space}"
  
      # --------------------------------------------------------------------
  
      def argsort(self, *args, **kwargs) -> np.ndarray:
          return np.lexsort((self.right, self.left))
  
      def equals(self, other) -> bool:
          """
          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(other)
  
          return (
              self.left.equals(other.left)
              and self.right.equals(other.right)
              and self.closed == other.closed
          )
  
      @Appender(Index.intersection.__doc__)
      @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
          -------
          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
          -------
          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
  
          other_tups = set(zip(other.left, other.right))
          for i, tup in enumerate(zip(self.left, self.right)):
              if tup in other_tups:
                  mask[i] = True
  
          return self[mask]
  
      def _setop(op_name: str, 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) -> bool:
          """
          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
  
      # GH#30817 until IntervalArray implements inequalities, get them from Index
      def __lt__(self, other):
          return Index.__lt__(self, other)
  
      def __le__(self, other):
          return Index.__le__(self, other)
  
      def __gt__(self, other):
          return Index.__gt__(self, other)
  
      def __ge__(self, other):
          return Index.__ge__(self, other)
  
  
  IntervalIndex._add_logical_methods_disabled()
  
  
  def _is_valid_endpoint(endpoint) -> bool:
      """
      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) -> bool:
      """
      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 : int, default None
          Number of periods to generate.
      freq : numeric, str, 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 : str, 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
      -------
      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
      <https://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):
          raise ValueError(f"start must be numeric or datetime-like, got {start}")
      elif not _is_valid_endpoint(end):
          raise ValueError(f"end must be numeric or datetime-like, got {end}")
  
      if is_float(periods):
          periods = int(periods)
      elif not is_integer(periods) and periods is not None:
          raise TypeError(f"periods must be a number, got {periods}")
  
      if freq is not None and not is_number(freq):
          try:
              freq = to_offset(freq)
          except ValueError as err:
              raise ValueError(
                  f"freq must be numeric or convertible to DateOffset, got {freq}"
              ) from err
  
      # 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)
  