text: from datetime import datetime, timedelta
  import operator
  from typing import (
      TYPE_CHECKING,
      Any,
      Callable,
      Optional,
      Sequence,
      Tuple,
      Type,
      TypeVar,
      Union,
      cast,
  )
  import warnings
  
  import numpy as np
  
  from pandas._libs import algos, lib
  from pandas._libs.tslibs import (
      BaseOffset,
      NaT,
      NaTType,
      Period,
      Resolution,
      Tick,
      Timestamp,
      delta_to_nanoseconds,
      iNaT,
      to_offset,
  )
  from pandas._libs.tslibs.timestamps import (
      RoundTo,
      integer_op_not_supported,
      round_nsint64,
  )
  from pandas._typing import DatetimeLikeScalar, DtypeObj
  from pandas.compat.numpy import function as nv
  from pandas.errors import AbstractMethodError, NullFrequencyError, PerformanceWarning
  from pandas.util._decorators import Appender, Substitution, cache_readonly
  
  from pandas.core.dtypes.common import (
      is_categorical_dtype,
      is_datetime64_any_dtype,
      is_datetime64_dtype,
      is_datetime64tz_dtype,
      is_datetime_or_timedelta_dtype,
      is_dtype_equal,
      is_extension_array_dtype,
      is_float_dtype,
      is_integer_dtype,
      is_list_like,
      is_object_dtype,
      is_period_dtype,
      is_string_dtype,
      is_timedelta64_dtype,
      is_unsigned_integer_dtype,
      pandas_dtype,
  )
  from pandas.core.dtypes.missing import is_valid_nat_for_dtype, isna
  
  from pandas.core import nanops, ops
  from pandas.core.algorithms import checked_add_with_arr, unique1d, value_counts
  from pandas.core.arraylike import OpsMixin
  from pandas.core.arrays._mixins import NDArrayBackedExtensionArray
  import pandas.core.common as com
  from pandas.core.construction import array, extract_array
  from pandas.core.indexers import check_array_indexer, check_setitem_lengths
  from pandas.core.ops.common import unpack_zerodim_and_defer
  from pandas.core.ops.invalid import invalid_comparison, make_invalid_op
  
  from pandas.tseries import frequencies
  
  if TYPE_CHECKING:
      from pandas.core.arrays import DatetimeArray, TimedeltaArray
  
  DTScalarOrNaT = Union[DatetimeLikeScalar, NaTType]
  DatetimeLikeArrayT = TypeVar("DatetimeLikeArrayT", bound="DatetimeLikeArrayMixin")
  
  
  class InvalidComparison(Exception):
      """
      Raised by _validate_comparison_value to indicate to caller it should
      return invalid_comparison.
      """
  
      pass
  
  
  class DatetimeLikeArrayMixin(OpsMixin, NDArrayBackedExtensionArray):
      """
      Shared Base/Mixin class for DatetimeArray, TimedeltaArray, PeriodArray
  
      Assumes that __new__/__init__ defines:
          _data
          _freq
  
      and that the inheriting class has methods:
          _generate_range
      """
  
      _is_recognized_dtype: Callable[[DtypeObj], bool]
      _recognized_scalars: Tuple[Type, ...]
      _data: np.ndarray
  
      def __init__(self, data, dtype=None, freq=None, copy=False):
          raise AbstractMethodError(self)
  
      @classmethod
      def _simple_new(
          cls, values: np.ndarray, freq: Optional[BaseOffset] = None, dtype=None
      ):
          raise AbstractMethodError(cls)
  
      @property
      def _scalar_type(self) -> Type[DatetimeLikeScalar]:
          """
          The scalar associated with this datelike
  
          * PeriodArray : Period
          * DatetimeArray : Timestamp
          * TimedeltaArray : Timedelta
          """
          raise AbstractMethodError(self)
  
      def _scalar_from_string(self, value: str) -> DTScalarOrNaT:
          """
          Construct a scalar type from a string.
  
          Parameters
          ----------
          value : str
  
          Returns
          -------
          Period, Timestamp, or Timedelta, or NaT
              Whatever the type of ``self._scalar_type`` is.
  
          Notes
          -----
          This should call ``self._check_compatible_with`` before
          unboxing the result.
          """
          raise AbstractMethodError(self)
  
      @classmethod
      def _rebox_native(cls, value: int) -> Union[int, np.datetime64, np.timedelta64]:
          """
          Box an integer unboxed via _unbox_scalar into the native type for
          the underlying ndarray.
          """
          raise AbstractMethodError(cls)
  
      def _unbox_scalar(
          self, value: DTScalarOrNaT, setitem: bool = False
      ) -> Union[np.int64, np.datetime64, np.timedelta64]:
          """
          Unbox the integer value of a scalar `value`.
  
          Parameters
          ----------
          value : Period, Timestamp, Timedelta, or NaT
              Depending on subclass.
          setitem : bool, default False
              Whether to check compatibility with setitem strictness.
  
          Returns
          -------
          int
  
          Examples
          --------
          >>> self._unbox_scalar(Timedelta("10s"))  # doctest: +SKIP
          10000000000
          """
          raise AbstractMethodError(self)
  
      def _check_compatible_with(
          self, other: DTScalarOrNaT, setitem: bool = False
      ) -> None:
          """
          Verify that `self` and `other` are compatible.
  
          * DatetimeArray verifies that the timezones (if any) match
          * PeriodArray verifies that the freq matches
          * Timedelta has no verification
  
          In each case, NaT is considered compatible.
  
          Parameters
          ----------
          other
          setitem : bool, default False
              For __setitem__ we may have stricter compatibility restrictions than
              for comparisons.
  
          Raises
          ------
          Exception
          """
          raise AbstractMethodError(self)
  
      # ------------------------------------------------------------------
      # NDArrayBackedExtensionArray compat
  
      @cache_readonly
      def _ndarray(self) -> np.ndarray:
          return self._data
  
      def _from_backing_data(
          self: DatetimeLikeArrayT, arr: np.ndarray
      ) -> DatetimeLikeArrayT:
          # Note: we do not retain `freq`
          return type(self)._simple_new(arr, dtype=self.dtype)
  
      # ------------------------------------------------------------------
  
      def _box_func(self, x):
          """
          box function to get object from internal representation
          """
          raise AbstractMethodError(self)
  
      def _box_values(self, values):
          """
          apply box func to passed values
          """
          return lib.map_infer(values, self._box_func)
  
      def __iter__(self):
          if self.ndim > 1:
              return (self[n] for n in range(len(self)))
          else:
              return (self._box_func(v) for v in self.asi8)
  
      @property
      def asi8(self) -> np.ndarray:
          """
          Integer representation of the values.
  
          Returns
          -------
          ndarray
              An ndarray with int64 dtype.
          """
          # do not cache or you'll create a memory leak
          return self._data.view("i8")
  
      # ----------------------------------------------------------------
      # Rendering Methods
  
      def _format_native_types(self, na_rep="NaT", date_format=None):
          """
          Helper method for astype when converting to strings.
  
          Returns
          -------
          ndarray[str]
          """
          raise AbstractMethodError(self)
  
      def _formatter(self, boxed=False):
          # TODO: Remove Datetime & DatetimeTZ formatters.
          return "'{}'".format
  
      # ----------------------------------------------------------------
      # Array-Like / EA-Interface Methods
  
      def __array__(self, dtype=None) -> np.ndarray:
          # used for Timedelta/DatetimeArray, overwritten by PeriodArray
          if is_object_dtype(dtype):
              return np.array(list(self), dtype=object)
          return self._ndarray
  
      def __getitem__(self, key):
          """
          This getitem defers to the underlying array, which by-definition can
          only handle list-likes, slices, and integer scalars
          """
          result = super().__getitem__(key)
          if lib.is_scalar(result):
              return result
  
          result._freq = self._get_getitem_freq(key)
          return result
  
      def _get_getitem_freq(self, key):
          """
          Find the `freq` attribute to assign to the result of a __getitem__ lookup.
          """
          is_period = is_period_dtype(self.dtype)
          if is_period:
              freq = self.freq
          elif self.ndim != 1:
              freq = None
          else:
              key = check_array_indexer(self, key)  # maybe ndarray[bool] -> slice
              freq = None
              if isinstance(key, slice):
                  if self.freq is not None and key.step is not None:
                      freq = key.step * self.freq
                  else:
                      freq = self.freq
              elif key is Ellipsis:
                  # GH#21282 indexing with Ellipsis is similar to a full slice,
                  #  should preserve `freq` attribute
                  freq = self.freq
              elif com.is_bool_indexer(key):
                  new_key = lib.maybe_booleans_to_slice(key.view(np.uint8))
                  if isinstance(new_key, slice):
                      return self._get_getitem_freq(new_key)
          return freq
  
      def __setitem__(
          self,
          key: Union[int, Sequence[int], Sequence[bool], slice],
          value: Union[NaTType, Any, Sequence[Any]],
      ) -> None:
          # I'm fudging the types a bit here. "Any" above really depends
          # on type(self). For PeriodArray, it's Period (or stuff coercible
          # to a period in from_sequence). For DatetimeArray, it's Timestamp...
          # I don't know if mypy can do that, possibly with Generics.
          # https://mypy.readthedocs.io/en/latest/generics.html
          no_op = check_setitem_lengths(key, value, self)
          if no_op:
              return
  
          super().__setitem__(key, value)
          self._maybe_clear_freq()
  
      def _maybe_clear_freq(self):
          # inplace operations like __setitem__ may invalidate the freq of
          # DatetimeArray and TimedeltaArray
          pass
  
      def astype(self, dtype, copy=True):
          # Some notes on cases we don't have to handle here in the base class:
          #   1. PeriodArray.astype handles period -> period
          #   2. DatetimeArray.astype handles conversion between tz.
          #   3. DatetimeArray.astype handles datetime -> period
          dtype = pandas_dtype(dtype)
  
          if is_object_dtype(dtype):
              return self._box_values(self.asi8.ravel()).reshape(self.shape)
          elif is_string_dtype(dtype) and not is_categorical_dtype(dtype):
              if is_extension_array_dtype(dtype):
                  arr_cls = dtype.construct_array_type()
                  return arr_cls._from_sequence(self, dtype=dtype)
              else:
                  return self._format_native_types()
          elif is_integer_dtype(dtype):
              # we deliberately ignore int32 vs. int64 here.
              # See https://github.com/pandas-dev/pandas/issues/24381 for more.
              values = self.asi8
  
              if is_unsigned_integer_dtype(dtype):
                  # Again, we ignore int32 vs. int64
                  values = values.view("uint64")
  
              if copy:
                  values = values.copy()
              return values
          elif (
              is_datetime_or_timedelta_dtype(dtype)
              and not is_dtype_equal(self.dtype, dtype)
          ) or is_float_dtype(dtype):
              # disallow conversion between datetime/timedelta,
              # and conversions for any datetimelike to float
              msg = f"Cannot cast {type(self).__name__} to dtype {dtype}"
              raise TypeError(msg)
          elif is_categorical_dtype(dtype):
              arr_cls = dtype.construct_array_type()
              return arr_cls(self, dtype=dtype)
          else:
              return np.asarray(self, dtype=dtype)
  
      def view(self, dtype=None):
          if dtype is None or dtype is self.dtype:
              return type(self)(self._ndarray, dtype=self.dtype)
          return self._ndarray.view(dtype=dtype)
  
      # ------------------------------------------------------------------
      # ExtensionArray Interface
  
      @classmethod
      def _concat_same_type(cls, to_concat, axis: int = 0):
          new_obj = super()._concat_same_type(to_concat, axis)
  
          obj = to_concat[0]
          dtype = obj.dtype
  
          new_freq = None
          if is_period_dtype(dtype):
              new_freq = obj.freq
          elif axis == 0:
              # GH 3232: If the concat result is evenly spaced, we can retain the
              # original frequency
              to_concat = [x for x in to_concat if len(x)]
  
              if obj.freq is not None and all(x.freq == obj.freq for x in to_concat):
                  pairs = zip(to_concat[:-1], to_concat[1:])
                  if all(pair[0][-1] + obj.freq == pair[1][0] for pair in pairs):
                      new_freq = obj.freq
  
          new_obj._freq = new_freq
          return new_obj
  
      def copy(self: DatetimeLikeArrayT) -> DatetimeLikeArrayT:
          new_obj = super().copy()
          new_obj._freq = self.freq
          return new_obj
  
      def _values_for_factorize(self):
          return self._ndarray, iNaT
  
      @classmethod
      def _from_factorized(cls, values, original):
          return cls(values, dtype=original.dtype)
  
      # ------------------------------------------------------------------
      # Validation Methods
      # TODO: try to de-duplicate these, ensure identical behavior
  
      def _validate_comparison_value(self, other):
          if isinstance(other, str):
              try:
                  # GH#18435 strings get a pass from tzawareness compat
                  other = self._scalar_from_string(other)
              except ValueError:
                  # failed to parse as Timestamp/Timedelta/Period
                  raise InvalidComparison(other)
  
          if isinstance(other, self._recognized_scalars) or other is NaT:
              other = self._scalar_type(other)
              try:
                  self._check_compatible_with(other)
              except TypeError as err:
                  # e.g. tzawareness mismatch
                  raise InvalidComparison(other) from err
  
          elif not is_list_like(other):
              raise InvalidComparison(other)
  
          elif len(other) != len(self):
              raise ValueError("Lengths must match")
  
          else:
              try:
                  other = self._validate_listlike(other, allow_object=True)
                  self._check_compatible_with(other)
              except TypeError as err:
                  if is_object_dtype(getattr(other, "dtype", None)):
                      # We will have to operate element-wise
                      pass
                  else:
                      raise InvalidComparison(other) from err
  
          return other
  
      def _validate_fill_value(self, fill_value):
          """
          If a fill_value is passed to `take` convert it to an i8 representation,
          raising ValueError if this is not possible.
  
          Parameters
          ----------
          fill_value : object
  
          Returns
          -------
          fill_value : np.int64, np.datetime64, or np.timedelta64
  
          Raises
          ------
          ValueError
          """
          msg = (
              f"'fill_value' should be a {self._scalar_type}. "
              f"Got '{str(fill_value)}'."
          )
          try:
              fill_value = self._validate_scalar(fill_value)
          except TypeError as err:
              raise ValueError(msg) from err
          return self._unbox(fill_value, setitem=True)
  
      def _validate_shift_value(self, fill_value):
          # TODO(2.0): once this deprecation is enforced, use _validate_fill_value
          if is_valid_nat_for_dtype(fill_value, self.dtype):
              fill_value = NaT
          elif isinstance(fill_value, self._recognized_scalars):
              fill_value = self._scalar_type(fill_value)
          else:
              # only warn if we're not going to raise
              if self._scalar_type is Period and lib.is_integer(fill_value):
                  # kludge for #31971 since Period(integer) tries to cast to str
                  new_fill = Period._from_ordinal(fill_value, freq=self.freq)
              else:
                  new_fill = self._scalar_type(fill_value)
  
              # stacklevel here is chosen to be correct when called from
              #  DataFrame.shift or Series.shift
              warnings.warn(
                  f"Passing {type(fill_value)} to shift is deprecated and "
                  "will raise in a future version, pass "
                  f"{self._scalar_type.__name__} instead.",
                  FutureWarning,
                  stacklevel=8,
              )
              fill_value = new_fill
  
          return self._unbox(fill_value, setitem=True)
  
      def _validate_scalar(self, value, allow_listlike: bool = False):
          """
          Validate that the input value can be cast to our scalar_type.
  
          Parameters
          ----------
          value : object
          allow_listlike: bool, default False
              When raising an exception, whether the message should say
              listlike inputs are allowed.
  
          Returns
          -------
          self._scalar_type or NaT
          """
          if isinstance(value, str):
              # NB: Careful about tzawareness
              try:
                  value = self._scalar_from_string(value)
              except ValueError as err:
                  msg = self._validation_error_message(value, allow_listlike)
                  raise TypeError(msg) from err
  
          elif is_valid_nat_for_dtype(value, self.dtype):
              # GH#18295
              value = NaT
  
          elif isinstance(value, self._recognized_scalars):
              # error: Too many arguments for "object"  [call-arg]
              value = self._scalar_type(value)  # type: ignore[call-arg]
  
          else:
              msg = self._validation_error_message(value, allow_listlike)
              raise TypeError(msg)
  
          return value
  
      def _validation_error_message(self, value, allow_listlike: bool = False) -> str:
          """
          Construct an exception message on validation error.
  
          Some methods allow only scalar inputs, while others allow either scalar
          or listlike.
  
          Parameters
          ----------
          allow_listlike: bool, default False
  
          Returns
          -------
          str
          """
          if allow_listlike:
              msg = (
                  f"value should be a '{self._scalar_type.__name__}', 'NaT', "
                  f"or array of those. Got '{type(value).__name__}' instead."
              )
          else:
              msg = (
                  f"value should be a '{self._scalar_type.__name__}' or 'NaT'. "
                  f"Got '{type(value).__name__}' instead."
              )
          return msg
  
      def _validate_listlike(self, value, allow_object: bool = False):
          if isinstance(value, type(self)):
              return value
  
          # Do type inference if necessary up front
          # e.g. we passed PeriodIndex.values and got an ndarray of Periods
          value = array(value)
          value = extract_array(value, extract_numpy=True)
  
          if is_dtype_equal(value.dtype, "string"):
              # We got a StringArray
              try:
                  # TODO: Could use from_sequence_of_strings if implemented
                  # Note: passing dtype is necessary for PeriodArray tests
                  value = type(self)._from_sequence(value, dtype=self.dtype)
              except ValueError:
                  pass
  
          if is_categorical_dtype(value.dtype):
              # e.g. we have a Categorical holding self.dtype
              if is_dtype_equal(value.categories.dtype, self.dtype):
                  # TODO: do we need equal dtype or just comparable?
                  value = value._internal_get_values()
                  value = extract_array(value, extract_numpy=True)
  
          if allow_object and is_object_dtype(value.dtype):
              pass
  
          elif not type(self)._is_recognized_dtype(value.dtype):
              msg = self._validation_error_message(value, True)
              raise TypeError(msg)
  
          return value
  
      def _validate_searchsorted_value(self, value):
          if not is_list_like(value):
              value = self._validate_scalar(value, True)
          else:
              value = self._validate_listlike(value)
  
          return self._unbox(value)
  
      def _validate_setitem_value(self, value):
          if is_list_like(value):
              value = self._validate_listlike(value)
          else:
              value = self._validate_scalar(value, True)
  
          return self._unbox(value, setitem=True)
  
      def _validate_insert_value(self, value):
          value = self._validate_scalar(value)
  
          return self._unbox(value, setitem=True)
  
      def _unbox(
          self, other, setitem: bool = False
      ) -> Union[np.int64, np.datetime64, np.timedelta64, np.ndarray]:
          """
          Unbox either a scalar with _unbox_scalar or an instance of our own type.
          """
          if lib.is_scalar(other):
              other = self._unbox_scalar(other, setitem=setitem)
          else:
              # same type as self
              self._check_compatible_with(other, setitem=setitem)
              other = other._ndarray
          return other
  
      # ------------------------------------------------------------------
      # Additional array methods
      #  These are not part of the EA API, but we implement them because
      #  pandas assumes they're there.
  
      def value_counts(self, dropna=False):
          """
          Return a Series containing counts of unique values.
  
          Parameters
          ----------
          dropna : bool, default True
              Don't include counts of NaT values.
  
          Returns
          -------
          Series
          """
          from pandas import Index, Series
  
          if dropna:
              values = self[~self.isna()]._ndarray
          else:
              values = self._ndarray
  
          cls = type(self)
  
          result = value_counts(values, sort=False, dropna=dropna)
          index = Index(
              cls(result.index.view("i8"), dtype=self.dtype), name=result.index.name
          )
          return Series(result._values, index=index, name=result.name)
  
      def map(self, mapper):
          # TODO(GH-23179): Add ExtensionArray.map
          # Need to figure out if we want ExtensionArray.map first.
          # If so, then we can refactor IndexOpsMixin._map_values to
          # a standalone function and call from here..
          # Else, just rewrite _map_infer_values to do the right thing.
          from pandas import Index
  
          return Index(self).map(mapper).array
  
      # ------------------------------------------------------------------
      # Null Handling
  
      def isna(self):
          return self._isnan
  
      @property  # NB: override with cache_readonly in immutable subclasses
      def _isnan(self):
          """
          return if each value is nan
          """
          return self.asi8 == iNaT
  
      @property  # NB: override with cache_readonly in immutable subclasses
      def _hasnans(self):
          """
          return if I have any nans; enables various perf speedups
          """
          return bool(self._isnan.any())
  
      def _maybe_mask_results(self, result, fill_value=iNaT, convert=None):
          """
          Parameters
          ----------
          result : a ndarray
          fill_value : object, default iNaT
          convert : str, dtype or None
  
          Returns
          -------
          result : ndarray with values replace by the fill_value
  
          mask the result if needed, convert to the provided dtype if its not
          None
  
          This is an internal routine.
          """
          if self._hasnans:
              if convert:
                  result = result.astype(convert)
              if fill_value is None:
                  fill_value = np.nan
              result[self._isnan] = fill_value
          return result
  
      # ------------------------------------------------------------------
      # Frequency Properties/Methods
  
      @property
      def freq(self):
          """
          Return the frequency object if it is set, otherwise None.
          """
          return self._freq
  
      @freq.setter
      def freq(self, value):
          if value is not None:
              value = to_offset(value)
              self._validate_frequency(self, value)
  
          self._freq = value
  
      @property
      def freqstr(self):
          """
          Return the frequency object as a string if its set, otherwise None.
          """
          if self.freq is None:
              return None
          return self.freq.freqstr
  
      @property  # NB: override with cache_readonly in immutable subclasses
      def inferred_freq(self):
          """
          Tries to return a string representing a frequency guess,
          generated by infer_freq.  Returns None if it can't autodetect the
          frequency.
          """
          if self.ndim != 1:
              return None
          try:
              return frequencies.infer_freq(self)
          except ValueError:
              return None
  
      @property  # NB: override with cache_readonly in immutable subclasses
      def _resolution_obj(self) -> Optional[Resolution]:
          try:
              return Resolution.get_reso_from_freq(self.freqstr)
          except KeyError:
              return None
  
      @property  # NB: override with cache_readonly in immutable subclasses
      def resolution(self) -> str:
          """
          Returns day, hour, minute, second, millisecond or microsecond
          """
          # error: Item "None" of "Optional[Any]" has no attribute "attrname"
          return self._resolution_obj.attrname  # type: ignore[union-attr]
  
      @classmethod
      def _validate_frequency(cls, index, freq, **kwargs):
          """
          Validate that a frequency is compatible with the values of a given
          Datetime Array/Index or Timedelta Array/Index
  
          Parameters
          ----------
          index : DatetimeIndex or TimedeltaIndex
              The index on which to determine if the given frequency is valid
          freq : DateOffset
              The frequency to validate
          """
          # TODO: this is not applicable to PeriodArray, move to correct Mixin
          inferred = index.inferred_freq
          if index.size == 0 or inferred == freq.freqstr:
              return None
  
          try:
              on_freq = cls._generate_range(
                  start=index[0], end=None, periods=len(index), freq=freq, **kwargs
              )
              if not np.array_equal(index.asi8, on_freq.asi8):
                  raise ValueError
          except ValueError as e:
              if "non-fixed" in str(e):
                  # non-fixed frequencies are not meaningful for timedelta64;
                  #  we retain that error message
                  raise e
              # GH#11587 the main way this is reached is if the `np.array_equal`
              #  check above is False.  This can also be reached if index[0]
              #  is `NaT`, in which case the call to `cls._generate_range` will
              #  raise a ValueError, which we re-raise with a more targeted
              #  message.
              raise ValueError(
                  f"Inferred frequency {inferred} from passed values "
                  f"does not conform to passed frequency {freq.freqstr}"
              ) from e
  
      @classmethod
      def _generate_range(cls, start, end, periods, freq, *args, **kwargs):
          raise AbstractMethodError(cls)
  
      # monotonicity/uniqueness properties are called via frequencies.infer_freq,
      #  see GH#23789
  
      @property
      def _is_monotonic_increasing(self):
          return algos.is_monotonic(self.asi8, timelike=True)[0]
  
      @property
      def _is_monotonic_decreasing(self):
          return algos.is_monotonic(self.asi8, timelike=True)[1]
  
      @property
      def _is_unique(self):
          return len(unique1d(self.asi8)) == len(self)
  
      # ------------------------------------------------------------------
      # Arithmetic Methods
  
      def _cmp_method(self, other, op):
          if self.ndim > 1 and getattr(other, "shape", None) == self.shape:
              # TODO: handle 2D-like listlikes
              return op(self.ravel(), other.ravel()).reshape(self.shape)
  
          try:
              other = self._validate_comparison_value(other)
          except InvalidComparison:
              return invalid_comparison(self, other, op)
  
          dtype = getattr(other, "dtype", None)
          if is_object_dtype(dtype):
              # We have to use comp_method_OBJECT_ARRAY instead of numpy
              #  comparison otherwise it would fail to raise when
              #  comparing tz-aware and tz-naive
              with np.errstate(all="ignore"):
                  result = ops.comp_method_OBJECT_ARRAY(
                      op, np.asarray(self.astype(object)), other
                  )
              return result
  
          other_vals = self._unbox(other)
          result = op(self._ndarray, other_vals)
  
          o_mask = isna(other)
          if self._hasnans | np.any(o_mask):
              nat_result = op is operator.ne
              result[self._isnan | o_mask] = nat_result
  
          return result
  
      # pow is invalid for all three subclasses; TimedeltaArray will override
      #  the multiplication and division ops
      __pow__ = make_invalid_op("__pow__")
      __rpow__ = make_invalid_op("__rpow__")
      __mul__ = make_invalid_op("__mul__")
      __rmul__ = make_invalid_op("__rmul__")
      __truediv__ = make_invalid_op("__truediv__")
      __rtruediv__ = make_invalid_op("__rtruediv__")
      __floordiv__ = make_invalid_op("__floordiv__")
      __rfloordiv__ = make_invalid_op("__rfloordiv__")
      __mod__ = make_invalid_op("__mod__")
      __rmod__ = make_invalid_op("__rmod__")
      __divmod__ = make_invalid_op("__divmod__")
      __rdivmod__ = make_invalid_op("__rdivmod__")
  
      def _add_datetimelike_scalar(self, other):
          # Overridden by TimedeltaArray
          raise TypeError(f"cannot add {type(self).__name__} and {type(other).__name__}")
  
      _add_datetime_arraylike = _add_datetimelike_scalar
  
      def _sub_datetimelike_scalar(self, other):
          # Overridden by DatetimeArray
          assert other is not NaT
          raise TypeError(f"cannot subtract a datelike from a {type(self).__name__}")
  
      _sub_datetime_arraylike = _sub_datetimelike_scalar
  
      def _sub_period(self, other):
          # Overridden by PeriodArray
          raise TypeError(f"cannot subtract Period from a {type(self).__name__}")
  
      def _add_period(self, other: Period):
          # Overridden by TimedeltaArray
          raise TypeError(f"cannot add Period to a {type(self).__name__}")
  
      def _add_offset(self, offset):
          raise AbstractMethodError(self)
  
      def _add_timedeltalike_scalar(self, other):
          """
          Add a delta of a timedeltalike
  
          Returns
          -------
          Same type as self
          """
          if isna(other):
              # i.e np.timedelta64("NaT"), not recognized by delta_to_nanoseconds
              new_values = np.empty(self.shape, dtype="i8")
              new_values[:] = iNaT
              return type(self)(new_values, dtype=self.dtype)
  
          inc = delta_to_nanoseconds(other)
          new_values = checked_add_with_arr(self.asi8, inc, arr_mask=self._isnan).view(
              "i8"
          )
          new_values = self._maybe_mask_results(new_values)
  
          new_freq = None
          if isinstance(self.freq, Tick) or is_period_dtype(self.dtype):
              # adding a scalar preserves freq
              new_freq = self.freq
  
          return type(self)(new_values, dtype=self.dtype, freq=new_freq)
  
      def _add_timedelta_arraylike(self, other):
          """
          Add a delta of a TimedeltaIndex
  
          Returns
          -------
          Same type as self
          """
          # overridden by PeriodArray
  
          if len(self) != len(other):
              raise ValueError("cannot add indices of unequal length")
  
          if isinstance(other, np.ndarray):
              # ndarray[timedelta64]; wrap in TimedeltaIndex for op
              from pandas.core.arrays import TimedeltaArray
  
              other = TimedeltaArray._from_sequence(other)
  
          self_i8 = self.asi8
          other_i8 = other.asi8
          new_values = checked_add_with_arr(
              self_i8, other_i8, arr_mask=self._isnan, b_mask=other._isnan
          )
          if self._hasnans or other._hasnans:
              mask = self._isnan | other._isnan
              new_values[mask] = iNaT
  
          return type(self)(new_values, dtype=self.dtype)
  
      def _add_nat(self):
          """
          Add pd.NaT to self
          """
          if is_period_dtype(self.dtype):
              raise TypeError(
                  f"Cannot add {type(self).__name__} and {type(NaT).__name__}"
              )
  
          # GH#19124 pd.NaT is treated like a timedelta for both timedelta
          # and datetime dtypes
          result = np.zeros(self.shape, dtype=np.int64)
          result.fill(iNaT)
          return type(self)(result, dtype=self.dtype, freq=None)
  
      def _sub_nat(self):
          """
          Subtract pd.NaT from self
          """
          # GH#19124 Timedelta - datetime is not in general well-defined.
          # We make an exception for pd.NaT, which in this case quacks
          # like a timedelta.
          # For datetime64 dtypes by convention we treat NaT as a datetime, so
          # this subtraction returns a timedelta64 dtype.
          # For period dtype, timedelta64 is a close-enough return dtype.
          result = np.zeros(self.shape, dtype=np.int64)
          result.fill(iNaT)
          return result.view("timedelta64[ns]")
  
      def _sub_period_array(self, other):
          # Overridden by PeriodArray
          raise TypeError(
              f"cannot subtract {other.dtype}-dtype from {type(self).__name__}"
          )
  
      def _addsub_object_array(self, other: np.ndarray, op):
          """
          Add or subtract array-like of DateOffset objects
  
          Parameters
          ----------
          other : np.ndarray[object]
          op : {operator.add, operator.sub}
  
          Returns
          -------
          result : same class as self
          """
          assert op in [operator.add, operator.sub]
          if len(other) == 1 and self.ndim == 1:
              # If both 1D then broadcasting is unambiguous
              return op(self, other[0])
  
          warnings.warn(
              "Adding/subtracting object-dtype array to "
              f"{type(self).__name__} not vectorized",
              PerformanceWarning,
          )
  
          # Caller is responsible for broadcasting if necessary
          assert self.shape == other.shape, (self.shape, other.shape)
  
          res_values = op(self.astype("O"), np.asarray(other))
          result = array(res_values.ravel())
          result = extract_array(result, extract_numpy=True).reshape(self.shape)
          return result
  
      def _time_shift(self, periods, freq=None):
          """
          Shift each value by `periods`.
  
          Note this is different from ExtensionArray.shift, which
          shifts the *position* of each element, padding the end with
          missing values.
  
          Parameters
          ----------
          periods : int
              Number of periods to shift by.
          freq : pandas.DateOffset, pandas.Timedelta, or str
              Frequency increment to shift by.
          """
          if freq is not None and freq != self.freq:
              if isinstance(freq, str):
                  freq = to_offset(freq)
              offset = periods * freq
              return self + offset
  
          if periods == 0 or len(self) == 0:
              # GH#14811 empty case
              return self.copy()
  
          if self.freq is None:
              raise NullFrequencyError("Cannot shift with no freq")
  
          start = self[0] + periods * self.freq
          end = self[-1] + periods * self.freq
  
          # Note: in the DatetimeTZ case, _generate_range will infer the
          #  appropriate timezone from `start` and `end`, so tz does not need
          #  to be passed explicitly.
          return self._generate_range(start=start, end=end, periods=None, freq=self.freq)
  
      @unpack_zerodim_and_defer("__add__")
      def __add__(self, other):
          other_dtype = getattr(other, "dtype", None)
  
          # scalar others
          if other is NaT:
              result = self._add_nat()
          elif isinstance(other, (Tick, timedelta, np.timedelta64)):
              result = self._add_timedeltalike_scalar(other)
          elif isinstance(other, BaseOffset):
              # specifically _not_ a Tick
              result = self._add_offset(other)
          elif isinstance(other, (datetime, np.datetime64)):
              result = self._add_datetimelike_scalar(other)
          elif isinstance(other, Period) and is_timedelta64_dtype(self.dtype):
              result = self._add_period(other)
          elif lib.is_integer(other):
              # This check must come after the check for np.timedelta64
              # as is_integer returns True for these
              if not is_period_dtype(self.dtype):
                  raise integer_op_not_supported(self)
              result = self._time_shift(other)
  
          # array-like others
          elif is_timedelta64_dtype(other_dtype):
              # TimedeltaIndex, ndarray[timedelta64]
              result = self._add_timedelta_arraylike(other)
          elif is_object_dtype(other_dtype):
              # e.g. Array/Index of DateOffset objects
              result = self._addsub_object_array(other, operator.add)
          elif is_datetime64_dtype(other_dtype) or is_datetime64tz_dtype(other_dtype):
              # DatetimeIndex, ndarray[datetime64]
              return self._add_datetime_arraylike(other)
          elif is_integer_dtype(other_dtype):
              if not is_period_dtype(self.dtype):
                  raise integer_op_not_supported(self)
              result = self._addsub_int_array(other, operator.add)
          else:
              # Includes Categorical, other ExtensionArrays
              # For PeriodDtype, if self is a TimedeltaArray and other is a
              #  PeriodArray with  a timedelta-like (i.e. Tick) freq, this
              #  operation is valid.  Defer to the PeriodArray implementation.
              #  In remaining cases, this will end up raising TypeError.
              return NotImplemented
  
          if isinstance(result, np.ndarray) and is_timedelta64_dtype(result.dtype):
              from pandas.core.arrays import TimedeltaArray
  
              return TimedeltaArray(result)
          return result
  
      def __radd__(self, other):
          # alias for __add__
          return self.__add__(other)
  
      @unpack_zerodim_and_defer("__sub__")
      def __sub__(self, other):
  
          other_dtype = getattr(other, "dtype", None)
  
          # scalar others
          if other is NaT:
              result = self._sub_nat()
          elif isinstance(other, (Tick, timedelta, np.timedelta64)):
              result = self._add_timedeltalike_scalar(-other)
          elif isinstance(other, BaseOffset):
              # specifically _not_ a Tick
              result = self._add_offset(-other)
          elif isinstance(other, (datetime, np.datetime64)):
              result = self._sub_datetimelike_scalar(other)
          elif lib.is_integer(other):
              # This check must come after the check for np.timedelta64
              # as is_integer returns True for these
              if not is_period_dtype(self.dtype):
                  raise integer_op_not_supported(self)
              result = self._time_shift(-other)
  
          elif isinstance(other, Period):
              result = self._sub_period(other)
  
          # array-like others
          elif is_timedelta64_dtype(other_dtype):
              # TimedeltaIndex, ndarray[timedelta64]
              result = self._add_timedelta_arraylike(-other)
          elif is_object_dtype(other_dtype):
              # e.g. Array/Index of DateOffset objects
              result = self._addsub_object_array(other, operator.sub)
          elif is_datetime64_dtype(other_dtype) or is_datetime64tz_dtype(other_dtype):
              # DatetimeIndex, ndarray[datetime64]
              result = self._sub_datetime_arraylike(other)
          elif is_period_dtype(other_dtype):
              # PeriodIndex
              result = self._sub_period_array(other)
          elif is_integer_dtype(other_dtype):
              if not is_period_dtype(self.dtype):
                  raise integer_op_not_supported(self)
              result = self._addsub_int_array(other, operator.sub)
          else:
              # Includes ExtensionArrays, float_dtype
              return NotImplemented
  
          if isinstance(result, np.ndarray) and is_timedelta64_dtype(result.dtype):
              from pandas.core.arrays import TimedeltaArray
  
              return TimedeltaArray(result)
          return result
  
      def __rsub__(self, other):
          other_dtype = getattr(other, "dtype", None)
  
          if is_datetime64_any_dtype(other_dtype) and is_timedelta64_dtype(self.dtype):
              # ndarray[datetime64] cannot be subtracted from self, so
              # we need to wrap in DatetimeArray/Index and flip the operation
              if lib.is_scalar(other):
                  # i.e. np.datetime64 object
                  return Timestamp(other) - self
              if not isinstance(other, DatetimeLikeArrayMixin):
                  # Avoid down-casting DatetimeIndex
                  from pandas.core.arrays import DatetimeArray
  
                  other = DatetimeArray(other)
              return other - self
          elif (
              is_datetime64_any_dtype(self.dtype)
              and hasattr(other, "dtype")
              and not is_datetime64_any_dtype(other.dtype)
          ):
              # GH#19959 datetime - datetime is well-defined as timedelta,
              # but any other type - datetime is not well-defined.
              raise TypeError(
                  f"cannot subtract {type(self).__name__} from {type(other).__name__}"
              )
          elif is_period_dtype(self.dtype) and is_timedelta64_dtype(other_dtype):
              # TODO: Can we simplify/generalize these cases at all?
              raise TypeError(f"cannot subtract {type(self).__name__} from {other.dtype}")
          elif is_timedelta64_dtype(self.dtype):
              self = cast("TimedeltaArray", self)
              return (-self) + other
  
          # We get here with e.g. datetime objects
          return -(self - other)
  
      def __iadd__(self, other):
          result = self + other
          self[:] = result[:]
  
          if not is_period_dtype(self.dtype):
              # restore freq, which is invalidated by setitem
              self._freq = result._freq
          return self
  
      def __isub__(self, other):
          result = self - other
          self[:] = result[:]
  
          if not is_period_dtype(self.dtype):
              # restore freq, which is invalidated by setitem
              self._freq = result._freq
          return self
  
      # --------------------------------------------------------------
      # Reductions
  
      def min(self, *, axis=None, skipna=True, **kwargs):
          """
          Return the minimum value of the Array or minimum along
          an axis.
  
          See Also
          --------
          numpy.ndarray.min
          Index.min : Return the minimum value in an Index.
          Series.min : Return the minimum value in a Series.
          """
          nv.validate_min((), kwargs)
          nv.validate_minmax_axis(axis, self.ndim)
  
          if is_period_dtype(self.dtype):
              # pass datetime64 values to nanops to get correct NaT semantics
              result = nanops.nanmin(
                  self._ndarray.view("M8[ns]"), axis=axis, skipna=skipna
              )
              if result is NaT:
                  return NaT
              result = result.view("i8")
              if axis is None or self.ndim == 1:
                  return self._box_func(result)
              return self._from_backing_data(result)
  
          result = nanops.nanmin(self._ndarray, axis=axis, skipna=skipna)
          if lib.is_scalar(result):
              return self._box_func(result)
          return self._from_backing_data(result)
  
      def max(self, *, axis=None, skipna=True, **kwargs):
          """
          Return the maximum value of the Array or maximum along
          an axis.
  
          See Also
          --------
          numpy.ndarray.max
          Index.max : Return the maximum value in an Index.
          Series.max : Return the maximum value in a Series.
          """
          # TODO: skipna is broken with max.
          # See https://github.com/pandas-dev/pandas/issues/24265
          nv.validate_max((), kwargs)
          nv.validate_minmax_axis(axis, self.ndim)
  
          if is_period_dtype(self.dtype):
              # pass datetime64 values to nanops to get correct NaT semantics
              result = nanops.nanmax(
                  self._ndarray.view("M8[ns]"), axis=axis, skipna=skipna
              )
              if result is NaT:
                  return result
              result = result.view("i8")
              if axis is None or self.ndim == 1:
                  return self._box_func(result)
              return self._from_backing_data(result)
  
          result = nanops.nanmax(self._ndarray, axis=axis, skipna=skipna)
          if lib.is_scalar(result):
              return self._box_func(result)
          return self._from_backing_data(result)
  
      def mean(self, *, skipna=True, axis: Optional[int] = 0):
          """
          Return the mean value of the Array.
  
          .. versionadded:: 0.25.0
  
          Parameters
          ----------
          skipna : bool, default True
              Whether to ignore any NaT elements.
          axis : int, optional, default 0
  
          Returns
          -------
          scalar
              Timestamp or Timedelta.
  
          See Also
          --------
          numpy.ndarray.mean : Returns the average of array elements along a given axis.
          Series.mean : Return the mean value in a Series.
  
          Notes
          -----
          mean is only defined for Datetime and Timedelta dtypes, not for Period.
          """
          if is_period_dtype(self.dtype):
              # See discussion in GH#24757
              raise TypeError(
                  f"mean is not implemented for {type(self).__name__} since the "
                  "meaning is ambiguous.  An alternative is "
                  "obj.to_timestamp(how='start').mean()"
              )
  
          result = nanops.nanmean(
              self._ndarray, axis=axis, skipna=skipna, mask=self.isna()
          )
          if axis is None or self.ndim == 1:
              return self._box_func(result)
          return self._from_backing_data(result)
  
      def median(self, *, axis: Optional[int] = None, skipna: bool = True, **kwargs):
          nv.validate_median((), kwargs)
  
          if axis is not None and abs(axis) >= self.ndim:
              raise ValueError("abs(axis) must be less than ndim")
  
          if is_period_dtype(self.dtype):
              # pass datetime64 values to nanops to get correct NaT semantics
              result = nanops.nanmedian(
                  self._ndarray.view("M8[ns]"), axis=axis, skipna=skipna
              )
              result = result.view("i8")
              if axis is None or self.ndim == 1:
                  return self._box_func(result)
              return self._from_backing_data(result)
  
          result = nanops.nanmedian(self._ndarray, axis=axis, skipna=skipna)
          if axis is None or self.ndim == 1:
              return self._box_func(result)
          return self._from_backing_data(result)
  
  
  class DatelikeOps(DatetimeLikeArrayMixin):
      """
      Common ops for DatetimeIndex/PeriodIndex, but not TimedeltaIndex.
      """
  
      @Substitution(
          URL="https://docs.python.org/3/library/datetime.html"
          "#strftime-and-strptime-behavior"
      )
      def strftime(self, date_format):
          """
          Convert to Index using specified date_format.
  
          Return an Index of formatted strings specified by date_format, which
          supports the same string format as the python standard library. Details
          of the string format can be found in `python string format
          doc <%(URL)s>`__.
  
          Parameters
          ----------
          date_format : str
              Date format string (e.g. "%%Y-%%m-%%d").
  
          Returns
          -------
          ndarray
              NumPy ndarray of formatted strings.
  
          See Also
          --------
          to_datetime : Convert the given argument to datetime.
          DatetimeIndex.normalize : Return DatetimeIndex with times to midnight.
          DatetimeIndex.round : Round the DatetimeIndex to the specified freq.
          DatetimeIndex.floor : Floor the DatetimeIndex to the specified freq.
  
          Examples
          --------
          >>> rng = pd.date_range(pd.Timestamp("2018-03-10 09:00"),
          ...                     periods=3, freq='s')
          >>> rng.strftime('%%B %%d, %%Y, %%r')
          Index(['March 10, 2018, 09:00:00 AM', 'March 10, 2018, 09:00:01 AM',
                 'March 10, 2018, 09:00:02 AM'],
                dtype='object')
          """
          result = self._format_native_types(date_format=date_format, na_rep=np.nan)
          return result.astype(object)
  
  
  _round_doc = """
      Perform {op} operation on the data to the specified `freq`.
  
      Parameters
      ----------
      freq : str or Offset
          The frequency level to {op} the index to. Must be a fixed
          frequency like 'S' (second) not 'ME' (month end). See
          :ref:`frequency aliases <timeseries.offset_aliases>` for
          a list of possible `freq` values.
      ambiguous : 'infer', bool-ndarray, 'NaT', default 'raise'
          Only relevant for DatetimeIndex:
  
          - 'infer' will attempt to infer fall dst-transition hours based on
            order
          - bool-ndarray where True signifies a DST time, False designates
            a non-DST time (note that this flag is only applicable for
            ambiguous times)
          - 'NaT' will return NaT where there are ambiguous times
          - 'raise' will raise an AmbiguousTimeError if there are ambiguous
            times.
  
          .. versionadded:: 0.24.0
  
      nonexistent : 'shift_forward', 'shift_backward', 'NaT', timedelta, default 'raise'
          A nonexistent time does not exist in a particular timezone
          where clocks moved forward due to DST.
  
          - 'shift_forward' will shift the nonexistent time forward to the
            closest existing time
          - 'shift_backward' will shift the nonexistent time backward to the
            closest existing time
          - 'NaT' will return NaT where there are nonexistent times
          - timedelta objects will shift nonexistent times by the timedelta
          - 'raise' will raise an NonExistentTimeError if there are
            nonexistent times.
  
          .. versionadded:: 0.24.0
  
      Returns
      -------
      DatetimeIndex, TimedeltaIndex, or Series
          Index of the same type for a DatetimeIndex or TimedeltaIndex,
          or a Series with the same index for a Series.
  
      Raises
      ------
      ValueError if the `freq` cannot be converted.
  
      Examples
      --------
      **DatetimeIndex**
  
      >>> rng = pd.date_range('1/1/2018 11:59:00', periods=3, freq='min')
      >>> rng
      DatetimeIndex(['2018-01-01 11:59:00', '2018-01-01 12:00:00',
                     '2018-01-01 12:01:00'],
                    dtype='datetime64[ns]', freq='T')
      """
  
  _round_example = """>>> rng.round('H')
      DatetimeIndex(['2018-01-01 12:00:00', '2018-01-01 12:00:00',
                     '2018-01-01 12:00:00'],
                    dtype='datetime64[ns]', freq=None)
  
      **Series**
  
      >>> pd.Series(rng).dt.round("H")
      0   2018-01-01 12:00:00
      1   2018-01-01 12:00:00
      2   2018-01-01 12:00:00
      dtype: datetime64[ns]
      """
  
  _floor_example = """>>> rng.floor('H')
      DatetimeIndex(['2018-01-01 11:00:00', '2018-01-01 12:00:00',
                     '2018-01-01 12:00:00'],
                    dtype='datetime64[ns]', freq=None)
  
      **Series**
  
      >>> pd.Series(rng).dt.floor("H")
      0   2018-01-01 11:00:00
      1   2018-01-01 12:00:00
      2   2018-01-01 12:00:00
      dtype: datetime64[ns]
      """
  
  _ceil_example = """>>> rng.ceil('H')
      DatetimeIndex(['2018-01-01 12:00:00', '2018-01-01 12:00:00',
                     '2018-01-01 13:00:00'],
                    dtype='datetime64[ns]', freq=None)
  
      **Series**
  
      >>> pd.Series(rng).dt.ceil("H")
      0   2018-01-01 12:00:00
      1   2018-01-01 12:00:00
      2   2018-01-01 13:00:00
      dtype: datetime64[ns]
      """
  
  
  class TimelikeOps(DatetimeLikeArrayMixin):
      """
      Common ops for TimedeltaIndex/DatetimeIndex, but not PeriodIndex.
      """
  
      def _round(self, freq, mode, ambiguous, nonexistent):
          # round the local times
          if is_datetime64tz_dtype(self.dtype):
              # operate on naive timestamps, then convert back to aware
              self = cast("DatetimeArray", self)
              naive = self.tz_localize(None)
              result = naive._round(freq, mode, ambiguous, nonexistent)
              return result.tz_localize(
                  self.tz, ambiguous=ambiguous, nonexistent=nonexistent
              )
  
          values = self.view("i8")
          result = round_nsint64(values, mode, freq)
          result = self._maybe_mask_results(result, fill_value=NaT)
          return self._simple_new(result, dtype=self.dtype)
  
      @Appender((_round_doc + _round_example).format(op="round"))
      def round(self, freq, ambiguous="raise", nonexistent="raise"):
          return self._round(freq, RoundTo.NEAREST_HALF_EVEN, ambiguous, nonexistent)
  
      @Appender((_round_doc + _floor_example).format(op="floor"))
      def floor(self, freq, ambiguous="raise", nonexistent="raise"):
          return self._round(freq, RoundTo.MINUS_INFTY, ambiguous, nonexistent)
  
      @Appender((_round_doc + _ceil_example).format(op="ceil"))
      def ceil(self, freq, ambiguous="raise", nonexistent="raise"):
          return self._round(freq, RoundTo.PLUS_INFTY, ambiguous, nonexistent)
  
      # --------------------------------------------------------------
      # Frequency Methods
  
      def _with_freq(self, freq):
          """
          Helper to get a view on the same data, with a new freq.
  
          Parameters
          ----------
          freq : DateOffset, None, or "infer"
  
          Returns
          -------
          Same type as self
          """
          # GH#29843
          if freq is None:
              # Always valid
              pass
          elif len(self) == 0 and isinstance(freq, BaseOffset):
              # Always valid.  In the TimedeltaArray case, we assume this
              #  is a Tick offset.
              pass
          else:
              # As an internal method, we can ensure this assertion always holds
              assert freq == "infer"
              freq = to_offset(self.inferred_freq)
  
          arr = self.view()
          arr._freq = freq
          return arr
  
  
  # -------------------------------------------------------------------
  # Shared Constructor Helpers
  
  
  def validate_periods(periods):
      """
      If a `periods` argument is passed to the Datetime/Timedelta Array/Index
      constructor, cast it to an integer.
  
      Parameters
      ----------
      periods : None, float, int
  
      Returns
      -------
      periods : None or int
  
      Raises
      ------
      TypeError
          if periods is None, float, or int
      """
      if periods is not None:
          if lib.is_float(periods):
              periods = int(periods)
          elif not lib.is_integer(periods):
              raise TypeError(f"periods must be a number, got {periods}")
      return periods
  
  
  def validate_endpoints(closed):
      """
      Check that the `closed` argument is among [None, "left", "right"]
  
      Parameters
      ----------
      closed : {None, "left", "right"}
  
      Returns
      -------
      left_closed : bool
      right_closed : bool
  
      Raises
      ------
      ValueError : if argument is not among valid values
      """
      left_closed = False
      right_closed = False
  
      if closed is None:
          left_closed = True
          right_closed = True
      elif closed == "left":
          left_closed = True
      elif closed == "right":
          right_closed = True
      else:
          raise ValueError("Closed has to be either 'left', 'right' or None")
  
      return left_closed, right_closed
  
  
  def validate_inferred_freq(freq, inferred_freq, freq_infer):
      """
      If the user passes a freq and another freq is inferred from passed data,
      require that they match.
  
      Parameters
      ----------
      freq : DateOffset or None
      inferred_freq : DateOffset or None
      freq_infer : bool
  
      Returns
      -------
      freq : DateOffset or None
      freq_infer : bool
  
      Notes
      -----
      We assume at this point that `maybe_infer_freq` has been called, so
      `freq` is either a DateOffset object or None.
      """
      if inferred_freq is not None:
          if freq is not None and freq != inferred_freq:
              raise ValueError(
                  f"Inferred frequency {inferred_freq} from passed "
                  "values does not conform to passed frequency "
                  f"{freq.freqstr}"
              )
          elif freq is None:
              freq = inferred_freq
          freq_infer = False
  
      return freq, freq_infer
  
  
  def maybe_infer_freq(freq):
      """
      Comparing a DateOffset to the string "infer" raises, so we need to
      be careful about comparisons.  Make a dummy variable `freq_infer` to
      signify the case where the given freq is "infer" and set freq to None
      to avoid comparison trouble later on.
  
      Parameters
      ----------
      freq : {DateOffset, None, str}
  
      Returns
      -------
      freq : {DateOffset, None}
      freq_infer : bool
          Whether we should inherit the freq of passed data.
      """
      freq_infer = False
      if not isinstance(freq, BaseOffset):
          # if a passed freq is None, don't infer automatically
          if freq != "infer":
              freq = to_offset(freq)
          else:
              freq_infer = True
              freq = None
      return freq, freq_infer
  