text: """
  Generic data algorithms. This module is experimental at the moment and not
  intended for public consumption
  """
  import operator
  from textwrap import dedent
  from typing import TYPE_CHECKING, Dict, Optional, Tuple, Union
  from warnings import catch_warnings, simplefilter, warn
  
  import numpy as np
  
  from pandas._libs import Timestamp, algos, hashtable as htable, iNaT, lib
  from pandas._typing import AnyArrayLike, ArrayLike, DtypeObj, FrameOrSeriesUnion
  from pandas.util._decorators import doc
  
  from pandas.core.dtypes.cast import (
      construct_1d_object_array_from_listlike,
      infer_dtype_from_array,
      maybe_promote,
  )
  from pandas.core.dtypes.common import (
      ensure_float64,
      ensure_int64,
      ensure_object,
      ensure_platform_int,
      ensure_uint64,
      is_array_like,
      is_bool_dtype,
      is_categorical_dtype,
      is_complex_dtype,
      is_datetime64_dtype,
      is_datetime64_ns_dtype,
      is_extension_array_dtype,
      is_float_dtype,
      is_integer,
      is_integer_dtype,
      is_list_like,
      is_numeric_dtype,
      is_object_dtype,
      is_period_dtype,
      is_scalar,
      is_signed_integer_dtype,
      is_timedelta64_dtype,
      is_unsigned_integer_dtype,
      needs_i8_conversion,
      pandas_dtype,
  )
  from pandas.core.dtypes.generic import (
      ABCExtensionArray,
      ABCIndex,
      ABCIndexClass,
      ABCMultiIndex,
      ABCSeries,
  )
  from pandas.core.dtypes.missing import isna, na_value_for_dtype
  
  from pandas.core.construction import array, extract_array
  from pandas.core.indexers import validate_indices
  
  if TYPE_CHECKING:
      from pandas import DataFrame, Series
  
  _shared_docs: Dict[str, str] = {}
  
  
  # --------------- #
  # dtype access    #
  # --------------- #
  def _ensure_data(
      values, dtype: Optional[DtypeObj] = None
  ) -> Tuple[np.ndarray, DtypeObj]:
      """
      routine to ensure that our data is of the correct
      input dtype for lower-level routines
  
      This will coerce:
      - ints -> int64
      - uint -> uint64
      - bool -> uint64 (TODO this should be uint8)
      - datetimelike -> i8
      - datetime64tz -> i8 (in local tz)
      - categorical -> codes
  
      Parameters
      ----------
      values : array-like
      dtype : pandas_dtype, optional
          coerce to this dtype
  
      Returns
      -------
      values : ndarray
      pandas_dtype : np.dtype or ExtensionDtype
      """
  
      if not isinstance(values, ABCMultiIndex):
          # extract_array would raise
          values = extract_array(values, extract_numpy=True)
  
      # we check some simple dtypes first
      if is_object_dtype(dtype):
          return ensure_object(np.asarray(values)), np.dtype("object")
      elif is_object_dtype(values) and dtype is None:
          return ensure_object(np.asarray(values)), np.dtype("object")
  
      try:
          if is_bool_dtype(values) or is_bool_dtype(dtype):
              # we are actually coercing to uint64
              # until our algos support uint8 directly (see TODO)
              return np.asarray(values).astype("uint64"), np.dtype("bool")
          elif is_signed_integer_dtype(values) or is_signed_integer_dtype(dtype):
              return ensure_int64(values), np.dtype("int64")
          elif is_unsigned_integer_dtype(values) or is_unsigned_integer_dtype(dtype):
              return ensure_uint64(values), np.dtype("uint64")
          elif is_float_dtype(values) or is_float_dtype(dtype):
              return ensure_float64(values), np.dtype("float64")
          elif is_complex_dtype(values) or is_complex_dtype(dtype):
  
              # ignore the fact that we are casting to float
              # which discards complex parts
              with catch_warnings():
                  simplefilter("ignore", np.ComplexWarning)
                  values = ensure_float64(values)
              return values, np.dtype("float64")
  
      except (TypeError, ValueError, OverflowError):
          # if we are trying to coerce to a dtype
          # and it is incompatible this will fall through to here
          return ensure_object(values), np.dtype("object")
  
      # datetimelike
      vals_dtype = getattr(values, "dtype", None)
      if needs_i8_conversion(vals_dtype) or needs_i8_conversion(dtype):
          if is_period_dtype(vals_dtype) or is_period_dtype(dtype):
              from pandas import PeriodIndex
  
              values = PeriodIndex(values)
              dtype = values.dtype
          elif is_timedelta64_dtype(vals_dtype) or is_timedelta64_dtype(dtype):
              from pandas import TimedeltaIndex
  
              values = TimedeltaIndex(values)
              dtype = values.dtype
          else:
              # Datetime
              if values.ndim > 1 and is_datetime64_ns_dtype(vals_dtype):
                  # Avoid calling the DatetimeIndex constructor as it is 1D only
                  # Note: this is reached by DataFrame.rank calls GH#27027
                  # TODO(EA2D): special case not needed with 2D EAs
                  asi8 = values.view("i8")
                  dtype = values.dtype
                  return asi8, dtype
  
              from pandas import DatetimeIndex
  
              values = DatetimeIndex(values)
              dtype = values.dtype
  
          return values.asi8, dtype
  
      elif is_categorical_dtype(vals_dtype) and (
          is_categorical_dtype(dtype) or dtype is None
      ):
          values = values.codes
          dtype = pandas_dtype("category")
  
          # we are actually coercing to int64
          # until our algos support int* directly (not all do)
          values = ensure_int64(values)
  
          return values, dtype
  
      # we have failed, return object
      values = np.asarray(values, dtype=object)
      return ensure_object(values), np.dtype("object")
  
  
  def _reconstruct_data(
      values: ArrayLike, dtype: DtypeObj, original: AnyArrayLike
  ) -> ArrayLike:
      """
      reverse of _ensure_data
  
      Parameters
      ----------
      values : np.ndarray or ExtensionArray
      dtype : np.ndtype or ExtensionDtype
      original : AnyArrayLike
  
      Returns
      -------
      ExtensionArray or np.ndarray
      """
      if is_extension_array_dtype(dtype):
          values = dtype.construct_array_type()._from_sequence(values)
      elif is_bool_dtype(dtype):
          values = values.astype(dtype, copy=False)
  
          # we only support object dtypes bool Index
          if isinstance(original, ABCIndexClass):
              values = values.astype(object, copy=False)
      elif dtype is not None:
          if is_datetime64_dtype(dtype):
              dtype = "datetime64[ns]"
          elif is_timedelta64_dtype(dtype):
              dtype = "timedelta64[ns]"
  
          values = values.astype(dtype, copy=False)
  
      return values
  
  
  def _ensure_arraylike(values):
      """
      ensure that we are arraylike if not already
      """
      if not is_array_like(values):
          inferred = lib.infer_dtype(values, skipna=False)
          if inferred in ["mixed", "string"]:
              if isinstance(values, tuple):
                  values = list(values)
              values = construct_1d_object_array_from_listlike(values)
          else:
              values = np.asarray(values)
      return values
  
  
  _hashtables = {
      "float64": htable.Float64HashTable,
      "uint64": htable.UInt64HashTable,
      "int64": htable.Int64HashTable,
      "string": htable.StringHashTable,
      "object": htable.PyObjectHashTable,
  }
  
  
  def _get_hashtable_algo(values):
      """
      Parameters
      ----------
      values : arraylike
  
      Returns
      -------
      htable : HashTable subclass
      values : ndarray
      """
      values, _ = _ensure_data(values)
  
      ndtype = _check_object_for_strings(values)
      htable = _hashtables[ndtype]
      return htable, values
  
  
  def _get_values_for_rank(values):
      if is_categorical_dtype(values):
          values = values._values_for_rank()
  
      values, _ = _ensure_data(values)
      return values
  
  
  def _get_data_algo(values):
      values = _get_values_for_rank(values)
  
      ndtype = _check_object_for_strings(values)
      htable = _hashtables.get(ndtype, _hashtables["object"])
  
      return htable, values
  
  
  def _check_object_for_strings(values) -> str:
      """
      Check if we can use string hashtable instead of object hashtable.
  
      Parameters
      ----------
      values : ndarray
      ndtype : str
  
      Returns
      -------
      str
      """
      ndtype = values.dtype.name
      if ndtype == "object":
  
          # it's cheaper to use a String Hash Table than Object; we infer
          # including nulls because that is the only difference between
          # StringHashTable and ObjectHashtable
          if lib.infer_dtype(values, skipna=False) in ["string"]:
              ndtype = "string"
      return ndtype
  
  
  # --------------- #
  # top-level algos #
  # --------------- #
  
  
  def unique(values):
      """
      Hash table-based unique. Uniques are returned in order
      of appearance. This does NOT sort.
  
      Significantly faster than numpy.unique. Includes NA values.
  
      Parameters
      ----------
      values : 1d array-like
  
      Returns
      -------
      numpy.ndarray or ExtensionArray
  
          The return can be:
  
          * Index : when the input is an Index
          * Categorical : when the input is a Categorical dtype
          * ndarray : when the input is a Series/ndarray
  
          Return numpy.ndarray or ExtensionArray.
  
      See Also
      --------
      Index.unique : Return unique values from an Index.
      Series.unique : Return unique values of Series object.
  
      Examples
      --------
      >>> pd.unique(pd.Series([2, 1, 3, 3]))
      array([2, 1, 3])
  
      >>> pd.unique(pd.Series([2] + [1] * 5))
      array([2, 1])
  
      >>> pd.unique(pd.Series([pd.Timestamp('20160101'),
      ...                     pd.Timestamp('20160101')]))
      array(['2016-01-01T00:00:00.000000000'], dtype='datetime64[ns]')
  
      >>> pd.unique(pd.Series([pd.Timestamp('20160101', tz='US/Eastern'),
      ...                      pd.Timestamp('20160101', tz='US/Eastern')]))
      array([Timestamp('2016-01-01 00:00:00-0500', tz='US/Eastern')],
            dtype=object)
  
      >>> pd.unique(pd.Index([pd.Timestamp('20160101', tz='US/Eastern'),
      ...                     pd.Timestamp('20160101', tz='US/Eastern')]))
      DatetimeIndex(['2016-01-01 00:00:00-05:00'],
      ...           dtype='datetime64[ns, US/Eastern]', freq=None)
  
      >>> pd.unique(list('baabc'))
      array(['b', 'a', 'c'], dtype=object)
  
      An unordered Categorical will return categories in the
      order of appearance.
  
      >>> pd.unique(pd.Series(pd.Categorical(list('baabc'))))
      [b, a, c]
      Categories (3, object): [b, a, c]
  
      >>> pd.unique(pd.Series(pd.Categorical(list('baabc'),
      ...                                    categories=list('abc'))))
      [b, a, c]
      Categories (3, object): [b, a, c]
  
      An ordered Categorical preserves the category ordering.
  
      >>> pd.unique(pd.Series(pd.Categorical(list('baabc'),
      ...                                    categories=list('abc'),
      ...                                    ordered=True)))
      [b, a, c]
      Categories (3, object): [a < b < c]
  
      An array of tuples
  
      >>> pd.unique([('a', 'b'), ('b', 'a'), ('a', 'c'), ('b', 'a')])
      array([('a', 'b'), ('b', 'a'), ('a', 'c')], dtype=object)
      """
      values = _ensure_arraylike(values)
  
      if is_extension_array_dtype(values):
          # Dispatch to extension dtype's unique.
          return values.unique()
  
      original = values
      htable, values = _get_hashtable_algo(values)
  
      table = htable(len(values))
      uniques = table.unique(values)
      uniques = _reconstruct_data(uniques, original.dtype, original)
      return uniques
  
  
  unique1d = unique
  
  
  def isin(comps: AnyArrayLike, values: AnyArrayLike) -> np.ndarray:
      """
      Compute the isin boolean array.
  
      Parameters
      ----------
      comps : array-like
      values : array-like
  
      Returns
      -------
      ndarray[bool]
          Same length as `comps`.
      """
      if not is_list_like(comps):
          raise TypeError(
              "only list-like objects are allowed to be passed "
              f"to isin(), you passed a [{type(comps).__name__}]"
          )
      if not is_list_like(values):
          raise TypeError(
              "only list-like objects are allowed to be passed "
              f"to isin(), you passed a [{type(values).__name__}]"
          )
  
      if not isinstance(values, (ABCIndex, ABCSeries, ABCExtensionArray, np.ndarray)):
          values = construct_1d_object_array_from_listlike(list(values))
          # TODO: could use ensure_arraylike here
  
      comps = extract_array(comps, extract_numpy=True)
      if is_categorical_dtype(comps):
          # TODO(extension)
          # handle categoricals
          # error: "ExtensionArray" has no attribute "isin"  [attr-defined]
          return comps.isin(values)  # type: ignore[attr-defined]
  
      comps, dtype = _ensure_data(comps)
      values, _ = _ensure_data(values, dtype=dtype)
  
      # faster for larger cases to use np.in1d
      f = htable.ismember_object
  
      # GH16012
      # Ensure np.in1d doesn't get object types or it *may* throw an exception
      if len(comps) > 1_000_000 and not is_object_dtype(comps):
          f = np.in1d
      elif is_integer_dtype(comps):
          try:
              values = values.astype("int64", copy=False)
              comps = comps.astype("int64", copy=False)
              f = htable.ismember_int64
          except (TypeError, ValueError, OverflowError):
              values = values.astype(object)
              comps = comps.astype(object)
  
      elif is_float_dtype(comps):
          try:
              values = values.astype("float64", copy=False)
              comps = comps.astype("float64", copy=False)
              f = htable.ismember_float64
          except (TypeError, ValueError):
              values = values.astype(object)
              comps = comps.astype(object)
  
      return f(comps, values)
  
  
  def _factorize_array(
      values, na_sentinel: int = -1, size_hint=None, na_value=None, mask=None
  ) -> Tuple[np.ndarray, np.ndarray]:
      """
      Factorize an array-like to codes and uniques.
  
      This doesn't do any coercion of types or unboxing before factorization.
  
      Parameters
      ----------
      values : ndarray
      na_sentinel : int, default -1
      size_hint : int, optional
          Passed through to the hashtable's 'get_labels' method
      na_value : object, optional
          A value in `values` to consider missing. Note: only use this
          parameter when you know that you don't have any values pandas would
          consider missing in the array (NaN for float data, iNaT for
          datetimes, etc.).
      mask : ndarray[bool], optional
          If not None, the mask is used as indicator for missing values
          (True = missing, False = valid) instead of `na_value` or
          condition "val != val".
  
      Returns
      -------
      codes : ndarray
      uniques : ndarray
      """
      hash_klass, values = _get_data_algo(values)
  
      table = hash_klass(size_hint or len(values))
      uniques, codes = table.factorize(
          values, na_sentinel=na_sentinel, na_value=na_value, mask=mask
      )
  
      codes = ensure_platform_int(codes)
      return codes, uniques
  
  
  @doc(
      values=dedent(
          """\
      values : sequence
          A 1-D sequence. Sequences that aren't pandas objects are
          coerced to ndarrays before factorization.
      """
      ),
      sort=dedent(
          """\
      sort : bool, default False
          Sort `uniques` and shuffle `codes` to maintain the
          relationship.
      """
      ),
      size_hint=dedent(
          """\
      size_hint : int, optional
          Hint to the hashtable sizer.
      """
      ),
  )
  def factorize(
      values,
      sort: bool = False,
      na_sentinel: Optional[int] = -1,
      size_hint: Optional[int] = None,
  ) -> Tuple[np.ndarray, Union[np.ndarray, ABCIndex]]:
      """
      Encode the object as an enumerated type or categorical variable.
  
      This method is useful for obtaining a numeric representation of an
      array when all that matters is identifying distinct values. `factorize`
      is available as both a top-level function :func:`pandas.factorize`,
      and as a method :meth:`Series.factorize` and :meth:`Index.factorize`.
  
      Parameters
      ----------
      {values}{sort}
      na_sentinel : int or None, default -1
          Value to mark "not found". If None, will not drop the NaN
          from the uniques of the values.
  
          .. versionchanged:: 1.1.2
      {size_hint}\
  
      Returns
      -------
      codes : ndarray
          An integer ndarray that's an indexer into `uniques`.
          ``uniques.take(codes)`` will have the same values as `values`.
      uniques : ndarray, Index, or Categorical
          The unique valid values. When `values` is Categorical, `uniques`
          is a Categorical. When `values` is some other pandas object, an
          `Index` is returned. Otherwise, a 1-D ndarray is returned.
  
          .. note ::
  
             Even if there's a missing value in `values`, `uniques` will
             *not* contain an entry for it.
  
      See Also
      --------
      cut : Discretize continuous-valued array.
      unique : Find the unique value in an array.
  
      Examples
      --------
      These examples all show factorize as a top-level method like
      ``pd.factorize(values)``. The results are identical for methods like
      :meth:`Series.factorize`.
  
      >>> codes, uniques = pd.factorize(['b', 'b', 'a', 'c', 'b'])
      >>> codes
      array([0, 0, 1, 2, 0]...)
      >>> uniques
      array(['b', 'a', 'c'], dtype=object)
  
      With ``sort=True``, the `uniques` will be sorted, and `codes` will be
      shuffled so that the relationship is the maintained.
  
      >>> codes, uniques = pd.factorize(['b', 'b', 'a', 'c', 'b'], sort=True)
      >>> codes
      array([1, 1, 0, 2, 1]...)
      >>> uniques
      array(['a', 'b', 'c'], dtype=object)
  
      Missing values are indicated in `codes` with `na_sentinel`
      (``-1`` by default). Note that missing values are never
      included in `uniques`.
  
      >>> codes, uniques = pd.factorize(['b', None, 'a', 'c', 'b'])
      >>> codes
      array([ 0, -1,  1,  2,  0]...)
      >>> uniques
      array(['b', 'a', 'c'], dtype=object)
  
      Thus far, we've only factorized lists (which are internally coerced to
      NumPy arrays). When factorizing pandas objects, the type of `uniques`
      will differ. For Categoricals, a `Categorical` is returned.
  
      >>> cat = pd.Categorical(['a', 'a', 'c'], categories=['a', 'b', 'c'])
      >>> codes, uniques = pd.factorize(cat)
      >>> codes
      array([0, 0, 1]...)
      >>> uniques
      ['a', 'c']
      Categories (3, object): ['a', 'b', 'c']
  
      Notice that ``'b'`` is in ``uniques.categories``, despite not being
      present in ``cat.values``.
  
      For all other pandas objects, an Index of the appropriate type is
      returned.
  
      >>> cat = pd.Series(['a', 'a', 'c'])
      >>> codes, uniques = pd.factorize(cat)
      >>> codes
      array([0, 0, 1]...)
      >>> uniques
      Index(['a', 'c'], dtype='object')
  
      If NaN is in the values, and we want to include NaN in the uniques of the
      values, it can be achieved by setting ``na_sentinel=None``.
  
      >>> values = np.array([1, 2, 1, np.nan])
      >>> codes, uniques = pd.factorize(values)  # default: na_sentinel=-1
      >>> codes
      array([ 0,  1,  0, -1])
      >>> uniques
      array([1., 2.])
  
      >>> codes, uniques = pd.factorize(values, na_sentinel=None)
      >>> codes
      array([0, 1, 0, 2])
      >>> uniques
      array([ 1.,  2., nan])
      """
      # Implementation notes: This method is responsible for 3 things
      # 1.) coercing data to array-like (ndarray, Index, extension array)
      # 2.) factorizing codes and uniques
      # 3.) Maybe boxing the uniques in an Index
      #
      # Step 2 is dispatched to extension types (like Categorical). They are
      # responsible only for factorization. All data coercion, sorting and boxing
      # should happen here.
  
      values = _ensure_arraylike(values)
      original = values
  
      # GH35667, if na_sentinel=None, we will not dropna NaNs from the uniques
      # of values, assign na_sentinel=-1 to replace code value for NaN.
      dropna = True
      if na_sentinel is None:
          na_sentinel = -1
          dropna = False
  
      if is_extension_array_dtype(values.dtype):
          values = extract_array(values)
          codes, uniques = values.factorize(na_sentinel=na_sentinel)
          dtype = original.dtype
      else:
          values, dtype = _ensure_data(values)
  
          if original.dtype.kind in ["m", "M"]:
              na_value = na_value_for_dtype(original.dtype)
          else:
              na_value = None
  
          codes, uniques = _factorize_array(
              values, na_sentinel=na_sentinel, size_hint=size_hint, na_value=na_value
          )
  
      if sort and len(uniques) > 0:
          uniques, codes = safe_sort(
              uniques, codes, na_sentinel=na_sentinel, assume_unique=True, verify=False
          )
  
      code_is_na = codes == na_sentinel
      if not dropna and code_is_na.any():
          # na_value is set based on the dtype of uniques, and compat set to False is
          # because we do not want na_value to be 0 for integers
          na_value = na_value_for_dtype(uniques.dtype, compat=False)
          uniques = np.append(uniques, [na_value])
          codes = np.where(code_is_na, len(uniques) - 1, codes)
  
      uniques = _reconstruct_data(uniques, dtype, original)
  
      # return original tenor
      if isinstance(original, ABCIndexClass):
          uniques = original._shallow_copy(uniques, name=None)
      elif isinstance(original, ABCSeries):
          from pandas import Index
  
          uniques = Index(uniques)
  
      return codes, uniques
  
  
  def value_counts(
      values,
      sort: bool = True,
      ascending: bool = False,
      normalize: bool = False,
      bins=None,
      dropna: bool = True,
  ) -> "Series":
      """
      Compute a histogram of the counts of non-null values.
  
      Parameters
      ----------
      values : ndarray (1-d)
      sort : bool, default True
          Sort by values
      ascending : bool, default False
          Sort in ascending order
      normalize: bool, default False
          If True then compute a relative histogram
      bins : integer, optional
          Rather than count values, group them into half-open bins,
          convenience for pd.cut, only works with numeric data
      dropna : bool, default True
          Don't include counts of NaN
  
      Returns
      -------
      Series
      """
      from pandas.core.series import Series
  
      name = getattr(values, "name", None)
  
      if bins is not None:
          from pandas.core.reshape.tile import cut
  
          values = Series(values)
          try:
              ii = cut(values, bins, include_lowest=True)
          except TypeError as err:
              raise TypeError("bins argument only works with numeric data.") from err
  
          # count, remove nulls (from the index), and but the bins
          result = ii.value_counts(dropna=dropna)
          result = result[result.index.notna()]
          result.index = result.index.astype("interval")
          result = result.sort_index()
  
          # if we are dropna and we have NO values
          if dropna and (result._values == 0).all():
              result = result.iloc[0:0]
  
          # normalizing is by len of all (regardless of dropna)
          counts = np.array([len(ii)])
  
      else:
  
          if is_extension_array_dtype(values):
  
              # handle Categorical and sparse,
              result = Series(values)._values.value_counts(dropna=dropna)
              result.name = name
              counts = result._values
  
          else:
              keys, counts = _value_counts_arraylike(values, dropna)
  
              result = Series(counts, index=keys, name=name)
  
      if sort:
          result = result.sort_values(ascending=ascending)
  
      if normalize:
          result = result / float(counts.sum())
  
      return result
  
  
  # Called once from SparseArray
  def _value_counts_arraylike(values, dropna: bool):
      """
      Parameters
      ----------
      values : arraylike
      dropna : bool
  
      Returns
      -------
      uniques : np.ndarray or ExtensionArray
      counts : np.ndarray
      """
      values = _ensure_arraylike(values)
      original = values
      values, _ = _ensure_data(values)
      ndtype = values.dtype.name
  
      if needs_i8_conversion(original.dtype):
          # datetime, timedelta, or period
  
          keys, counts = htable.value_count_int64(values, dropna)
  
          if dropna:
              msk = keys != iNaT
              keys, counts = keys[msk], counts[msk]
  
      else:
          # ndarray like
  
          # TODO: handle uint8
          f = getattr(htable, f"value_count_{ndtype}")
          keys, counts = f(values, dropna)
  
          mask = isna(values)
          if not dropna and mask.any():
              if not isna(keys).any():
                  keys = np.insert(keys, 0, np.NaN)
                  counts = np.insert(counts, 0, mask.sum())
  
      keys = _reconstruct_data(keys, original.dtype, original)
  
      return keys, counts
  
  
  def duplicated(values, keep="first") -> np.ndarray:
      """
      Return boolean ndarray denoting duplicate values.
  
      Parameters
      ----------
      values : ndarray-like
          Array over which to check for duplicate values.
      keep : {'first', 'last', False}, default 'first'
          - ``first`` : Mark duplicates as ``True`` except for the first
            occurrence.
          - ``last`` : Mark duplicates as ``True`` except for the last
            occurrence.
          - False : Mark all duplicates as ``True``.
  
      Returns
      -------
      duplicated : ndarray
      """
      values, _ = _ensure_data(values)
      ndtype = values.dtype.name
      f = getattr(htable, f"duplicated_{ndtype}")
      return f(values, keep=keep)
  
  
  def mode(values, dropna: bool = True) -> "Series":
      """
      Returns the mode(s) of an array.
  
      Parameters
      ----------
      values : array-like
          Array over which to check for duplicate values.
      dropna : boolean, default True
          Don't consider counts of NaN/NaT.
  
          .. versionadded:: 0.24.0
  
      Returns
      -------
      mode : Series
      """
      from pandas import Series
  
      values = _ensure_arraylike(values)
      original = values
  
      # categorical is a fast-path
      if is_categorical_dtype(values):
          if isinstance(values, Series):
              # TODO: should we be passing `name` below?
              return Series(values._values.mode(dropna=dropna), name=values.name)
          return values.mode(dropna=dropna)
  
      if dropna and needs_i8_conversion(values.dtype):
          mask = values.isnull()
          values = values[~mask]
  
      values, _ = _ensure_data(values)
      ndtype = values.dtype.name
  
      f = getattr(htable, f"mode_{ndtype}")
      result = f(values, dropna=dropna)
      try:
          result = np.sort(result)
      except TypeError as err:
          warn(f"Unable to sort modes: {err}")
  
      result = _reconstruct_data(result, original.dtype, original)
      return Series(result)
  
  
  def rank(
      values,
      axis: int = 0,
      method: str = "average",
      na_option: str = "keep",
      ascending: bool = True,
      pct: bool = False,
  ):
      """
      Rank the values along a given axis.
  
      Parameters
      ----------
      values : array-like
          Array whose values will be ranked. The number of dimensions in this
          array must not exceed 2.
      axis : int, default 0
          Axis over which to perform rankings.
      method : {'average', 'min', 'max', 'first', 'dense'}, default 'average'
          The method by which tiebreaks are broken during the ranking.
      na_option : {'keep', 'top'}, default 'keep'
          The method by which NaNs are placed in the ranking.
          - ``keep``: rank each NaN value with a NaN ranking
          - ``top``: replace each NaN with either +/- inf so that they
                     there are ranked at the top
      ascending : boolean, default True
          Whether or not the elements should be ranked in ascending order.
      pct : boolean, default False
          Whether or not to the display the returned rankings in integer form
          (e.g. 1, 2, 3) or in percentile form (e.g. 0.333..., 0.666..., 1).
      """
      if values.ndim == 1:
          values = _get_values_for_rank(values)
          ranks = algos.rank_1d(
              values,
              ties_method=method,
              ascending=ascending,
              na_option=na_option,
              pct=pct,
          )
      elif values.ndim == 2:
          values = _get_values_for_rank(values)
          ranks = algos.rank_2d(
              values,
              axis=axis,
              ties_method=method,
              ascending=ascending,
              na_option=na_option,
              pct=pct,
          )
      else:
          raise TypeError("Array with ndim > 2 are not supported.")
  
      return ranks
  
  
  def checked_add_with_arr(arr, b, arr_mask=None, b_mask=None):
      """
      Perform array addition that checks for underflow and overflow.
  
      Performs the addition of an int64 array and an int64 integer (or array)
      but checks that they do not result in overflow first. For elements that
      are indicated to be NaN, whether or not there is overflow for that element
      is automatically ignored.
  
      Parameters
      ----------
      arr : array addend.
      b : array or scalar addend.
      arr_mask : boolean array or None
          array indicating which elements to exclude from checking
      b_mask : boolean array or boolean or None
          array or scalar indicating which element(s) to exclude from checking
  
      Returns
      -------
      sum : An array for elements x + b for each element x in arr if b is
            a scalar or an array for elements x + y for each element pair
            (x, y) in (arr, b).
  
      Raises
      ------
      OverflowError if any x + y exceeds the maximum or minimum int64 value.
      """
      # For performance reasons, we broadcast 'b' to the new array 'b2'
      # so that it has the same size as 'arr'.
      b2 = np.broadcast_to(b, arr.shape)
      if b_mask is not None:
          # We do the same broadcasting for b_mask as well.
          b2_mask = np.broadcast_to(b_mask, arr.shape)
      else:
          b2_mask = None
  
      # For elements that are NaN, regardless of their value, we should
      # ignore whether they overflow or not when doing the checked add.
      if arr_mask is not None and b2_mask is not None:
          not_nan = np.logical_not(arr_mask | b2_mask)
      elif arr_mask is not None:
          not_nan = np.logical_not(arr_mask)
      elif b_mask is not None:
          not_nan = np.logical_not(b2_mask)
      else:
          not_nan = np.empty(arr.shape, dtype=bool)
          not_nan.fill(True)
  
      # gh-14324: For each element in 'arr' and its corresponding element
      # in 'b2', we check the sign of the element in 'b2'. If it is positive,
      # we then check whether its sum with the element in 'arr' exceeds
      # np.iinfo(np.int64).max. If so, we have an overflow error. If it
      # it is negative, we then check whether its sum with the element in
      # 'arr' exceeds np.iinfo(np.int64).min. If so, we have an overflow
      # error as well.
      mask1 = b2 > 0
      mask2 = b2 < 0
  
      if not mask1.any():
          to_raise = ((np.iinfo(np.int64).min - b2 > arr) & not_nan).any()
      elif not mask2.any():
          to_raise = ((np.iinfo(np.int64).max - b2 < arr) & not_nan).any()
      else:
          to_raise = (
              ((np.iinfo(np.int64).max - b2[mask1] < arr[mask1]) & not_nan[mask1]).any()
              or (
                  (np.iinfo(np.int64).min - b2[mask2] > arr[mask2]) & not_nan[mask2]
              ).any()
          )
  
      if to_raise:
          raise OverflowError("Overflow in int64 addition")
      return arr + b
  
  
  def quantile(x, q, interpolation_method="fraction"):
      """
      Compute sample quantile or quantiles of the input array. For example, q=0.5
      computes the median.
  
      The `interpolation_method` parameter supports three values, namely
      `fraction` (default), `lower` and `higher`. Interpolation is done only,
      if the desired quantile lies between two data points `i` and `j`. For
      `fraction`, the result is an interpolated value between `i` and `j`;
      for `lower`, the result is `i`, for `higher` the result is `j`.
  
      Parameters
      ----------
      x : ndarray
          Values from which to extract score.
      q : scalar or array
          Percentile at which to extract score.
      interpolation_method : {'fraction', 'lower', 'higher'}, optional
          This optional parameter specifies the interpolation method to use,
          when the desired quantile lies between two data points `i` and `j`:
  
          - fraction: `i + (j - i)*fraction`, where `fraction` is the
                      fractional part of the index surrounded by `i` and `j`.
          -lower: `i`.
          - higher: `j`.
  
      Returns
      -------
      score : float
          Score at percentile.
  
      Examples
      --------
      >>> from scipy import stats
      >>> a = np.arange(100)
      >>> stats.scoreatpercentile(a, 50)
      49.5
  
      """
      x = np.asarray(x)
      mask = isna(x)
  
      x = x[~mask]
  
      values = np.sort(x)
  
      def _interpolate(a, b, fraction):
          """
          Returns the point at the given fraction between a and b, where
          'fraction' must be between 0 and 1.
          """
          return a + (b - a) * fraction
  
      def _get_score(at):
          if len(values) == 0:
              return np.nan
  
          idx = at * (len(values) - 1)
          if idx % 1 == 0:
              score = values[int(idx)]
          else:
              if interpolation_method == "fraction":
                  score = _interpolate(values[int(idx)], values[int(idx) + 1], idx % 1)
              elif interpolation_method == "lower":
                  score = values[np.floor(idx)]
              elif interpolation_method == "higher":
                  score = values[np.ceil(idx)]
              else:
                  raise ValueError(
                      "interpolation_method can only be 'fraction' "
                      ", 'lower' or 'higher'"
                  )
  
          return score
  
      if is_scalar(q):
          return _get_score(q)
      else:
          q = np.asarray(q, np.float64)
          result = [_get_score(x) for x in q]
          result = np.array(result, dtype=np.float64)
          return result
  
  
  # --------------- #
  # select n        #
  # --------------- #
  
  
  class SelectN:
      def __init__(self, obj, n: int, keep: str):
          self.obj = obj
          self.n = n
          self.keep = keep
  
          if self.keep not in ("first", "last", "all"):
              raise ValueError('keep must be either "first", "last" or "all"')
  
      def compute(self, method: str) -> FrameOrSeriesUnion:
          raise NotImplementedError
  
      def nlargest(self):
          return self.compute("nlargest")
  
      def nsmallest(self):
          return self.compute("nsmallest")
  
      @staticmethod
      def is_valid_dtype_n_method(dtype: DtypeObj) -> bool:
          """
          Helper function to determine if dtype is valid for
          nsmallest/nlargest methods
          """
          return (
              is_numeric_dtype(dtype) and not is_complex_dtype(dtype)
          ) or needs_i8_conversion(dtype)
  
  
  class SelectNSeries(SelectN):
      """
      Implement n largest/smallest for Series
  
      Parameters
      ----------
      obj : Series
      n : int
      keep : {'first', 'last'}, default 'first'
  
      Returns
      -------
      nordered : Series
      """
  
      def compute(self, method: str) -> "Series":
  
          n = self.n
          dtype = self.obj.dtype
          if not self.is_valid_dtype_n_method(dtype):
              raise TypeError(f"Cannot use method '{method}' with dtype {dtype}")
  
          if n <= 0:
              return self.obj[[]]
  
          dropped = self.obj.dropna()
  
          # slow method
          if n >= len(self.obj):
              reverse_it = self.keep == "last" or method == "nlargest"
              ascending = method == "nsmallest"
              slc = np.s_[::-1] if reverse_it else np.s_[:]
              return dropped[slc].sort_values(ascending=ascending).head(n)
  
          # fast method
          arr, pandas_dtype = _ensure_data(dropped.values)
          if method == "nlargest":
              arr = -arr
              if is_integer_dtype(pandas_dtype):
                  # GH 21426: ensure reverse ordering at boundaries
                  arr -= 1
  
              elif is_bool_dtype(pandas_dtype):
                  # GH 26154: ensure False is smaller than True
                  arr = 1 - (-arr)
  
          if self.keep == "last":
              arr = arr[::-1]
  
          narr = len(arr)
          n = min(n, narr)
  
          kth_val = algos.kth_smallest(arr.copy(), n - 1)
          (ns,) = np.nonzero(arr <= kth_val)
          inds = ns[arr[ns].argsort(kind="mergesort")]
  
          if self.keep != "all":
              inds = inds[:n]
  
          if self.keep == "last":
              # reverse indices
              inds = narr - 1 - inds
  
          return dropped.iloc[inds]
  
  
  class SelectNFrame(SelectN):
      """
      Implement n largest/smallest for DataFrame
  
      Parameters
      ----------
      obj : DataFrame
      n : int
      keep : {'first', 'last'}, default 'first'
      columns : list or str
  
      Returns
      -------
      nordered : DataFrame
      """
  
      def __init__(self, obj, n: int, keep: str, columns):
          super().__init__(obj, n, keep)
          if not is_list_like(columns) or isinstance(columns, tuple):
              columns = [columns]
          columns = list(columns)
          self.columns = columns
  
      def compute(self, method: str) -> "DataFrame":
  
          from pandas import Int64Index
  
          n = self.n
          frame = self.obj
          columns = self.columns
  
          for column in columns:
              dtype = frame[column].dtype
              if not self.is_valid_dtype_n_method(dtype):
                  raise TypeError(
                      f"Column {repr(column)} has dtype {dtype}, "
                      f"cannot use method {repr(method)} with this dtype"
                  )
  
          def get_indexer(current_indexer, other_indexer):
              """
              Helper function to concat `current_indexer` and `other_indexer`
              depending on `method`
              """
              if method == "nsmallest":
                  return current_indexer.append(other_indexer)
              else:
                  return other_indexer.append(current_indexer)
  
          # Below we save and reset the index in case index contains duplicates
          original_index = frame.index
          cur_frame = frame = frame.reset_index(drop=True)
          cur_n = n
          indexer = Int64Index([])
  
          for i, column in enumerate(columns):
              # For each column we apply method to cur_frame[column].
              # If it's the last column or if we have the number of
              # results desired we are done.
              # Otherwise there are duplicates of the largest/smallest
              # value and we need to look at the rest of the columns
              # to determine which of the rows with the largest/smallest
              # value in the column to keep.
              series = cur_frame[column]
              is_last_column = len(columns) - 1 == i
              values = getattr(series, method)(
                  cur_n, keep=self.keep if is_last_column else "all"
              )
  
              if is_last_column or len(values) <= cur_n:
                  indexer = get_indexer(indexer, values.index)
                  break
  
              # Now find all values which are equal to
              # the (nsmallest: largest)/(nlargest: smallest)
              # from our series.
              border_value = values == values[values.index[-1]]
  
              # Some of these values are among the top-n
              # some aren't.
              unsafe_values = values[border_value]
  
              # These values are definitely among the top-n
              safe_values = values[~border_value]
              indexer = get_indexer(indexer, safe_values.index)
  
              # Go on and separate the unsafe_values on the remaining
              # columns.
              cur_frame = cur_frame.loc[unsafe_values.index]
              cur_n = n - len(indexer)
  
          frame = frame.take(indexer)
  
          # Restore the index on frame
          frame.index = original_index.take(indexer)
  
          # If there is only one column, the frame is already sorted.
          if len(columns) == 1:
              return frame
  
          ascending = method == "nsmallest"
  
          return frame.sort_values(columns, ascending=ascending, kind="mergesort")
  
  
  # ---- #
  # take #
  # ---- #
  
  
  def _view_wrapper(f, arr_dtype=None, out_dtype=None, fill_wrap=None):
      def wrapper(arr, indexer, out, fill_value=np.nan):
          if arr_dtype is not None:
              arr = arr.view(arr_dtype)
          if out_dtype is not None:
              out = out.view(out_dtype)
          if fill_wrap is not None:
              fill_value = fill_wrap(fill_value)
          f(arr, indexer, out, fill_value=fill_value)
  
      return wrapper
  
  
  def _convert_wrapper(f, conv_dtype):
      def wrapper(arr, indexer, out, fill_value=np.nan):
          arr = arr.astype(conv_dtype)
          f(arr, indexer, out, fill_value=fill_value)
  
      return wrapper
  
  
  def _take_2d_multi_object(arr, indexer, out, fill_value, mask_info):
      # this is not ideal, performance-wise, but it's better than raising
      # an exception (best to optimize in Cython to avoid getting here)
      row_idx, col_idx = indexer
      if mask_info is not None:
          (row_mask, col_mask), (row_needs, col_needs) = mask_info
      else:
          row_mask = row_idx == -1
          col_mask = col_idx == -1
          row_needs = row_mask.any()
          col_needs = col_mask.any()
      if fill_value is not None:
          if row_needs:
              out[row_mask, :] = fill_value
          if col_needs:
              out[:, col_mask] = fill_value
      for i in range(len(row_idx)):
          u_ = row_idx[i]
          for j in range(len(col_idx)):
              v = col_idx[j]
              out[i, j] = arr[u_, v]
  
  
  def _take_nd_object(arr, indexer, out, axis: int, fill_value, mask_info):
      if mask_info is not None:
          mask, needs_masking = mask_info
      else:
          mask = indexer == -1
          needs_masking = mask.any()
      if arr.dtype != out.dtype:
          arr = arr.astype(out.dtype)
      if arr.shape[axis] > 0:
          arr.take(ensure_platform_int(indexer), axis=axis, out=out)
      if needs_masking:
          outindexer = [slice(None)] * arr.ndim
          outindexer[axis] = mask
          out[tuple(outindexer)] = fill_value
  
  
  _take_1d_dict = {
      ("int8", "int8"): algos.take_1d_int8_int8,
      ("int8", "int32"): algos.take_1d_int8_int32,
      ("int8", "int64"): algos.take_1d_int8_int64,
      ("int8", "float64"): algos.take_1d_int8_float64,
      ("int16", "int16"): algos.take_1d_int16_int16,
      ("int16", "int32"): algos.take_1d_int16_int32,
      ("int16", "int64"): algos.take_1d_int16_int64,
      ("int16", "float64"): algos.take_1d_int16_float64,
      ("int32", "int32"): algos.take_1d_int32_int32,
      ("int32", "int64"): algos.take_1d_int32_int64,
      ("int32", "float64"): algos.take_1d_int32_float64,
      ("int64", "int64"): algos.take_1d_int64_int64,
      ("int64", "float64"): algos.take_1d_int64_float64,
      ("float32", "float32"): algos.take_1d_float32_float32,
      ("float32", "float64"): algos.take_1d_float32_float64,
      ("float64", "float64"): algos.take_1d_float64_float64,
      ("object", "object"): algos.take_1d_object_object,
      ("bool", "bool"): _view_wrapper(algos.take_1d_bool_bool, np.uint8, np.uint8),
      ("bool", "object"): _view_wrapper(algos.take_1d_bool_object, np.uint8, None),
      ("datetime64[ns]", "datetime64[ns]"): _view_wrapper(
          algos.take_1d_int64_int64, np.int64, np.int64, np.int64
      ),
  }
  
  _take_2d_axis0_dict = {
      ("int8", "int8"): algos.take_2d_axis0_int8_int8,
      ("int8", "int32"): algos.take_2d_axis0_int8_int32,
      ("int8", "int64"): algos.take_2d_axis0_int8_int64,
      ("int8", "float64"): algos.take_2d_axis0_int8_float64,
      ("int16", "int16"): algos.take_2d_axis0_int16_int16,
      ("int16", "int32"): algos.take_2d_axis0_int16_int32,
      ("int16", "int64"): algos.take_2d_axis0_int16_int64,
      ("int16", "float64"): algos.take_2d_axis0_int16_float64,
      ("int32", "int32"): algos.take_2d_axis0_int32_int32,
      ("int32", "int64"): algos.take_2d_axis0_int32_int64,
      ("int32", "float64"): algos.take_2d_axis0_int32_float64,
      ("int64", "int64"): algos.take_2d_axis0_int64_int64,
      ("int64", "float64"): algos.take_2d_axis0_int64_float64,
      ("float32", "float32"): algos.take_2d_axis0_float32_float32,
      ("float32", "float64"): algos.take_2d_axis0_float32_float64,
      ("float64", "float64"): algos.take_2d_axis0_float64_float64,
      ("object", "object"): algos.take_2d_axis0_object_object,
      ("bool", "bool"): _view_wrapper(algos.take_2d_axis0_bool_bool, np.uint8, np.uint8),
      ("bool", "object"): _view_wrapper(algos.take_2d_axis0_bool_object, np.uint8, None),
      ("datetime64[ns]", "datetime64[ns]"): _view_wrapper(
          algos.take_2d_axis0_int64_int64, np.int64, np.int64, fill_wrap=np.int64
      ),
  }
  
  _take_2d_axis1_dict = {
      ("int8", "int8"): algos.take_2d_axis1_int8_int8,
      ("int8", "int32"): algos.take_2d_axis1_int8_int32,
      ("int8", "int64"): algos.take_2d_axis1_int8_int64,
      ("int8", "float64"): algos.take_2d_axis1_int8_float64,
      ("int16", "int16"): algos.take_2d_axis1_int16_int16,
      ("int16", "int32"): algos.take_2d_axis1_int16_int32,
      ("int16", "int64"): algos.take_2d_axis1_int16_int64,
      ("int16", "float64"): algos.take_2d_axis1_int16_float64,
      ("int32", "int32"): algos.take_2d_axis1_int32_int32,
      ("int32", "int64"): algos.take_2d_axis1_int32_int64,
      ("int32", "float64"): algos.take_2d_axis1_int32_float64,
      ("int64", "int64"): algos.take_2d_axis1_int64_int64,
      ("int64", "float64"): algos.take_2d_axis1_int64_float64,
      ("float32", "float32"): algos.take_2d_axis1_float32_float32,
      ("float32", "float64"): algos.take_2d_axis1_float32_float64,
      ("float64", "float64"): algos.take_2d_axis1_float64_float64,
      ("object", "object"): algos.take_2d_axis1_object_object,
      ("bool", "bool"): _view_wrapper(algos.take_2d_axis1_bool_bool, np.uint8, np.uint8),
      ("bool", "object"): _view_wrapper(algos.take_2d_axis1_bool_object, np.uint8, None),
      ("datetime64[ns]", "datetime64[ns]"): _view_wrapper(
          algos.take_2d_axis1_int64_int64, np.int64, np.int64, fill_wrap=np.int64
      ),
  }
  
  _take_2d_multi_dict = {
      ("int8", "int8"): algos.take_2d_multi_int8_int8,
      ("int8", "int32"): algos.take_2d_multi_int8_int32,
      ("int8", "int64"): algos.take_2d_multi_int8_int64,
      ("int8", "float64"): algos.take_2d_multi_int8_float64,
      ("int16", "int16"): algos.take_2d_multi_int16_int16,
      ("int16", "int32"): algos.take_2d_multi_int16_int32,
      ("int16", "int64"): algos.take_2d_multi_int16_int64,
      ("int16", "float64"): algos.take_2d_multi_int16_float64,
      ("int32", "int32"): algos.take_2d_multi_int32_int32,
      ("int32", "int64"): algos.take_2d_multi_int32_int64,
      ("int32", "float64"): algos.take_2d_multi_int32_float64,
      ("int64", "int64"): algos.take_2d_multi_int64_int64,
      ("int64", "float64"): algos.take_2d_multi_int64_float64,
      ("float32", "float32"): algos.take_2d_multi_float32_float32,
      ("float32", "float64"): algos.take_2d_multi_float32_float64,
      ("float64", "float64"): algos.take_2d_multi_float64_float64,
      ("object", "object"): algos.take_2d_multi_object_object,
      ("bool", "bool"): _view_wrapper(algos.take_2d_multi_bool_bool, np.uint8, np.uint8),
      ("bool", "object"): _view_wrapper(algos.take_2d_multi_bool_object, np.uint8, None),
      ("datetime64[ns]", "datetime64[ns]"): _view_wrapper(
          algos.take_2d_multi_int64_int64, np.int64, np.int64, fill_wrap=np.int64
      ),
  }
  
  
  def _get_take_nd_function(
      ndim: int, arr_dtype, out_dtype, axis: int = 0, mask_info=None
  ):
      if ndim <= 2:
          tup = (arr_dtype.name, out_dtype.name)
          if ndim == 1:
              func = _take_1d_dict.get(tup, None)
          elif ndim == 2:
              if axis == 0:
                  func = _take_2d_axis0_dict.get(tup, None)
              else:
                  func = _take_2d_axis1_dict.get(tup, None)
          if func is not None:
              return func
  
          tup = (out_dtype.name, out_dtype.name)
          if ndim == 1:
              func = _take_1d_dict.get(tup, None)
          elif ndim == 2:
              if axis == 0:
                  func = _take_2d_axis0_dict.get(tup, None)
              else:
                  func = _take_2d_axis1_dict.get(tup, None)
          if func is not None:
              func = _convert_wrapper(func, out_dtype)
              return func
  
      def func2(arr, indexer, out, fill_value=np.nan):
          indexer = ensure_int64(indexer)
          _take_nd_object(
              arr, indexer, out, axis=axis, fill_value=fill_value, mask_info=mask_info
          )
  
      return func2
  
  
  def take(arr, indices, axis: int = 0, allow_fill: bool = False, fill_value=None):
      """
      Take elements from an array.
  
      .. versionadded:: 0.23.0
  
      Parameters
      ----------
      arr : sequence
          Non array-likes (sequences without a dtype) are coerced
          to an ndarray.
      indices : sequence of integers
          Indices to be taken.
      axis : int, default 0
          The axis over which to select values.
      allow_fill : bool, default False
          How to handle negative values in `indices`.
  
          * False: negative values in `indices` indicate positional indices
            from the right (the default). This is similar to :func:`numpy.take`.
  
          * True: negative values in `indices` indicate
            missing values. These values are set to `fill_value`. Any other
            other negative values raise a ``ValueError``.
  
      fill_value : any, optional
          Fill value to use for NA-indices when `allow_fill` is True.
          This may be ``None``, in which case the default NA value for
          the type (``self.dtype.na_value``) is used.
  
          For multi-dimensional `arr`, each *element* is filled with
          `fill_value`.
  
      Returns
      -------
      ndarray or ExtensionArray
          Same type as the input.
  
      Raises
      ------
      IndexError
          When `indices` is out of bounds for the array.
      ValueError
          When the indexer contains negative values other than ``-1``
          and `allow_fill` is True.
  
      Notes
      -----
      When `allow_fill` is False, `indices` may be whatever dimensionality
      is accepted by NumPy for `arr`.
  
      When `allow_fill` is True, `indices` should be 1-D.
  
      See Also
      --------
      numpy.take : Take elements from an array along an axis.
  
      Examples
      --------
      >>> from pandas.api.extensions import take
  
      With the default ``allow_fill=False``, negative numbers indicate
      positional indices from the right.
  
      >>> take(np.array([10, 20, 30]), [0, 0, -1])
      array([10, 10, 30])
  
      Setting ``allow_fill=True`` will place `fill_value` in those positions.
  
      >>> take(np.array([10, 20, 30]), [0, 0, -1], allow_fill=True)
      array([10., 10., nan])
  
      >>> take(np.array([10, 20, 30]), [0, 0, -1], allow_fill=True,
      ...      fill_value=-10)
      array([ 10,  10, -10])
      """
      if not is_array_like(arr):
          arr = np.asarray(arr)
  
      indices = np.asarray(indices, dtype=np.intp)
  
      if allow_fill:
          # Pandas style, -1 means NA
          validate_indices(indices, arr.shape[axis])
          result = take_1d(
              arr, indices, axis=axis, allow_fill=True, fill_value=fill_value
          )
      else:
          # NumPy style
          result = arr.take(indices, axis=axis)
      return result
  
  
  def take_nd(
      arr, indexer, axis: int = 0, out=None, fill_value=np.nan, allow_fill: bool = True
  ):
      """
      Specialized Cython take which sets NaN values in one pass
  
      This dispatches to ``take`` defined on ExtensionArrays. It does not
      currently dispatch to ``SparseArray.take`` for sparse ``arr``.
  
      Parameters
      ----------
      arr : array-like
          Input array.
      indexer : ndarray
          1-D array of indices to take, subarrays corresponding to -1 value
          indices are filed with fill_value
      axis : int, default 0
          Axis to take from
      out : ndarray or None, default None
          Optional output array, must be appropriate type to hold input and
          fill_value together, if indexer has any -1 value entries; call
          maybe_promote to determine this type for any fill_value
      fill_value : any, default np.nan
          Fill value to replace -1 values with
      allow_fill : boolean, default True
          If False, indexer is assumed to contain no -1 values so no filling
          will be done.  This short-circuits computation of a mask.  Result is
          undefined if allow_fill == False and -1 is present in indexer.
  
      Returns
      -------
      subarray : array-like
          May be the same type as the input, or cast to an ndarray.
      """
      mask_info = None
  
      if is_extension_array_dtype(arr):
          return arr.take(indexer, fill_value=fill_value, allow_fill=allow_fill)
  
      arr = extract_array(arr)
      arr = np.asarray(arr)
  
      if indexer is None:
          indexer = np.arange(arr.shape[axis], dtype=np.int64)
          dtype, fill_value = arr.dtype, arr.dtype.type()
      else:
          indexer = ensure_int64(indexer, copy=False)
          if not allow_fill:
              dtype, fill_value = arr.dtype, arr.dtype.type()
              mask_info = None, False
          else:
              # check for promotion based on types only (do this first because
              # it's faster than computing a mask)
              dtype, fill_value = maybe_promote(arr.dtype, fill_value)
              if dtype != arr.dtype and (out is None or out.dtype != dtype):
                  # check if promotion is actually required based on indexer
                  mask = indexer == -1
                  needs_masking = mask.any()
                  mask_info = mask, needs_masking
                  if needs_masking:
                      if out is not None and out.dtype != dtype:
                          raise TypeError("Incompatible type for fill_value")
                  else:
                      # if not, then depromote, set fill_value to dummy
                      # (it won't be used but we don't want the cython code
                      # to crash when trying to cast it to dtype)
                      dtype, fill_value = arr.dtype, arr.dtype.type()
  
      flip_order = False
      if arr.ndim == 2:
          if arr.flags.f_contiguous:
              flip_order = True
  
      if flip_order:
          arr = arr.T
          axis = arr.ndim - axis - 1
          if out is not None:
              out = out.T
  
      # at this point, it's guaranteed that dtype can hold both the arr values
      # and the fill_value
      if out is None:
          out_shape_ = list(arr.shape)
          out_shape_[axis] = len(indexer)
          out_shape = tuple(out_shape_)
          if arr.flags.f_contiguous and axis == arr.ndim - 1:
              # minor tweak that can make an order-of-magnitude difference
              # for dataframes initialized directly from 2-d ndarrays
              # (s.t. df.values is c-contiguous and df._mgr.blocks[0] is its
              # f-contiguous transpose)
              out = np.empty(out_shape, dtype=dtype, order="F")
          else:
              out = np.empty(out_shape, dtype=dtype)
  
      func = _get_take_nd_function(
          arr.ndim, arr.dtype, out.dtype, axis=axis, mask_info=mask_info
      )
      func(arr, indexer, out, fill_value)
  
      if flip_order:
          out = out.T
      return out
  
  
  take_1d = take_nd
  
  
  def take_2d_multi(arr, indexer, fill_value=np.nan):
      """
      Specialized Cython take which sets NaN values in one pass.
      """
      # This is only called from one place in DataFrame._reindex_multi,
      #  so we know indexer is well-behaved.
      assert indexer is not None
      assert indexer[0] is not None
      assert indexer[1] is not None
  
      row_idx, col_idx = indexer
  
      row_idx = ensure_int64(row_idx)
      col_idx = ensure_int64(col_idx)
      indexer = row_idx, col_idx
      mask_info = None
  
      # check for promotion based on types only (do this first because
      # it's faster than computing a mask)
      dtype, fill_value = maybe_promote(arr.dtype, fill_value)
      if dtype != arr.dtype:
          # check if promotion is actually required based on indexer
          row_mask = row_idx == -1
          col_mask = col_idx == -1
          row_needs = row_mask.any()
          col_needs = col_mask.any()
          mask_info = (row_mask, col_mask), (row_needs, col_needs)
  
          if not (row_needs or col_needs):
              # if not, then depromote, set fill_value to dummy
              # (it won't be used but we don't want the cython code
              # to crash when trying to cast it to dtype)
              dtype, fill_value = arr.dtype, arr.dtype.type()
  
      # at this point, it's guaranteed that dtype can hold both the arr values
      # and the fill_value
      out_shape = len(row_idx), len(col_idx)
      out = np.empty(out_shape, dtype=dtype)
  
      func = _take_2d_multi_dict.get((arr.dtype.name, out.dtype.name), None)
      if func is None and arr.dtype != out.dtype:
          func = _take_2d_multi_dict.get((out.dtype.name, out.dtype.name), None)
          if func is not None:
              func = _convert_wrapper(func, out.dtype)
      if func is None:
  
          def func(arr, indexer, out, fill_value=np.nan):
              _take_2d_multi_object(
                  arr, indexer, out, fill_value=fill_value, mask_info=mask_info
              )
  
      func(arr, indexer, out=out, fill_value=fill_value)
      return out
  
  
  # ------------ #
  # searchsorted #
  # ------------ #
  
  
  def searchsorted(arr, value, side="left", sorter=None):
      """
      Find indices where elements should be inserted to maintain order.
  
      .. versionadded:: 0.25.0
  
      Find the indices into a sorted array `arr` (a) such that, if the
      corresponding elements in `value` were inserted before the indices,
      the order of `arr` would be preserved.
  
      Assuming that `arr` is sorted:
  
      ======  ================================
      `side`  returned index `i` satisfies
      ======  ================================
      left    ``arr[i-1] < value <= self[i]``
      right   ``arr[i-1] <= value < self[i]``
      ======  ================================
  
      Parameters
      ----------
      arr: array-like
          Input array. If `sorter` is None, then it must be sorted in
          ascending order, otherwise `sorter` must be an array of indices
          that sort it.
      value : array_like
          Values to insert into `arr`.
      side : {'left', 'right'}, optional
          If 'left', the index of the first suitable location found is given.
          If 'right', return the last such index.  If there is no suitable
          index, return either 0 or N (where N is the length of `self`).
      sorter : 1-D array_like, optional
          Optional array of integer indices that sort array a into ascending
          order. They are typically the result of argsort.
  
      Returns
      -------
      array of ints
          Array of insertion points with the same shape as `value`.
  
      See Also
      --------
      numpy.searchsorted : Similar method from NumPy.
      """
      if sorter is not None:
          sorter = ensure_platform_int(sorter)
  
      if (
          isinstance(arr, np.ndarray)
          and is_integer_dtype(arr)
          and (is_integer(value) or is_integer_dtype(value))
      ):
          # if `arr` and `value` have different dtypes, `arr` would be
          # recast by numpy, causing a slow search.
          # Before searching below, we therefore try to give `value` the
          # same dtype as `arr`, while guarding against integer overflows.
          iinfo = np.iinfo(arr.dtype.type)
          value_arr = np.array([value]) if is_scalar(value) else np.array(value)
          if (value_arr >= iinfo.min).all() and (value_arr <= iinfo.max).all():
              # value within bounds, so no overflow, so can convert value dtype
              # to dtype of arr
              dtype = arr.dtype
          else:
              dtype = value_arr.dtype
  
          if is_scalar(value):
              value = dtype.type(value)
          else:
              value = array(value, dtype=dtype)
      elif not (
          is_object_dtype(arr) or is_numeric_dtype(arr) or is_categorical_dtype(arr)
      ):
          # E.g. if `arr` is an array with dtype='datetime64[ns]'
          # and `value` is a pd.Timestamp, we may need to convert value
          value_ser = array([value]) if is_scalar(value) else array(value)
          value = value_ser[0] if is_scalar(value) else value_ser
          if isinstance(value, Timestamp) and value.tzinfo is None:
              value = value.to_datetime64()
  
      result = arr.searchsorted(value, side=side, sorter=sorter)
      return result
  
  
  # ---- #
  # diff #
  # ---- #
  
  _diff_special = {"float64", "float32", "int64", "int32", "int16", "int8"}
  
  
  def diff(arr, n: int, axis: int = 0, stacklevel=3):
      """
      difference of n between self,
      analogous to s-s.shift(n)
  
      Parameters
      ----------
      arr : ndarray
      n : int
          number of periods
      axis : int
          axis to shift on
      stacklevel : int
          The stacklevel for the lost dtype warning.
  
      Returns
      -------
      shifted
      """
      from pandas.core.arrays import PandasDtype
  
      n = int(n)
      na = np.nan
      dtype = arr.dtype
  
      if dtype.kind == "b":
          op = operator.xor
      else:
          op = operator.sub
  
      if isinstance(dtype, PandasDtype):
          # PandasArray cannot necessarily hold shifted versions of itself.
          arr = np.asarray(arr)
          dtype = arr.dtype
  
      if is_extension_array_dtype(dtype):
          if hasattr(arr, f"__{op.__name__}__"):
              return op(arr, arr.shift(n))
          else:
              warn(
                  "dtype lost in 'diff()'. In the future this will raise a "
                  "TypeError. Convert to a suitable dtype prior to calling 'diff'.",
                  FutureWarning,
                  stacklevel=stacklevel,
              )
              arr = np.asarray(arr)
              dtype = arr.dtype
  
      is_timedelta = False
      is_bool = False
      if needs_i8_conversion(arr.dtype):
          dtype = np.float64
          arr = arr.view("i8")
          na = iNaT
          is_timedelta = True
  
      elif is_bool_dtype(dtype):
          dtype = np.object_
          is_bool = True
  
      elif is_integer_dtype(dtype):
          dtype = np.float64
  
      dtype = np.dtype(dtype)
      out_arr = np.empty(arr.shape, dtype=dtype)
  
      na_indexer = [slice(None)] * arr.ndim
      na_indexer[axis] = slice(None, n) if n >= 0 else slice(n, None)
      out_arr[tuple(na_indexer)] = na
  
      if arr.ndim == 2 and arr.dtype.name in _diff_special:
          # TODO: can diff_2d dtype specialization troubles be fixed by defining
          #  out_arr inside diff_2d?
          algos.diff_2d(arr, out_arr, n, axis)
      else:
          # To keep mypy happy, _res_indexer is a list while res_indexer is
          #  a tuple, ditto for lag_indexer.
          _res_indexer = [slice(None)] * arr.ndim
          _res_indexer[axis] = slice(n, None) if n >= 0 else slice(None, n)
          res_indexer = tuple(_res_indexer)
  
          _lag_indexer = [slice(None)] * arr.ndim
          _lag_indexer[axis] = slice(None, -n) if n > 0 else slice(-n, None)
          lag_indexer = tuple(_lag_indexer)
  
          # need to make sure that we account for na for datelike/timedelta
          # we don't actually want to subtract these i8 numbers
          if is_timedelta:
              res = arr[res_indexer]
              lag = arr[lag_indexer]
  
              mask = (arr[res_indexer] == na) | (arr[lag_indexer] == na)
              if mask.any():
                  res = res.copy()
                  res[mask] = 0
                  lag = lag.copy()
                  lag[mask] = 0
  
              result = res - lag
              result[mask] = na
              out_arr[res_indexer] = result
          elif is_bool:
              out_arr[res_indexer] = arr[res_indexer] ^ arr[lag_indexer]
          else:
              out_arr[res_indexer] = arr[res_indexer] - arr[lag_indexer]
  
      if is_timedelta:
          out_arr = out_arr.astype("int64").view("timedelta64[ns]")
  
      return out_arr
  
  
  # --------------------------------------------------------------------
  # Helper functions
  
  # Note: safe_sort is in algorithms.py instead of sorting.py because it is
  #  low-dependency, is used in this module, and used private methods from
  #  this module.
  def safe_sort(
      values,
      codes=None,
      na_sentinel: int = -1,
      assume_unique: bool = False,
      verify: bool = True,
  ) -> Union[np.ndarray, Tuple[np.ndarray, np.ndarray]]:
      """
      Sort ``values`` and reorder corresponding ``codes``.
  
      ``values`` should be unique if ``codes`` is not None.
      Safe for use with mixed types (int, str), orders ints before strs.
  
      Parameters
      ----------
      values : list-like
          Sequence; must be unique if ``codes`` is not None.
      codes : list_like, optional
          Indices to ``values``. All out of bound indices are treated as
          "not found" and will be masked with ``na_sentinel``.
      na_sentinel : int, default -1
          Value in ``codes`` to mark "not found".
          Ignored when ``codes`` is None.
      assume_unique : bool, default False
          When True, ``values`` are assumed to be unique, which can speed up
          the calculation. Ignored when ``codes`` is None.
      verify : bool, default True
          Check if codes are out of bound for the values and put out of bound
          codes equal to na_sentinel. If ``verify=False``, it is assumed there
          are no out of bound codes. Ignored when ``codes`` is None.
  
          .. versionadded:: 0.25.0
  
      Returns
      -------
      ordered : ndarray
          Sorted ``values``
      new_codes : ndarray
          Reordered ``codes``; returned when ``codes`` is not None.
  
      Raises
      ------
      TypeError
          * If ``values`` is not list-like or if ``codes`` is neither None
          nor list-like
          * If ``values`` cannot be sorted
      ValueError
          * If ``codes`` is not None and ``values`` contain duplicates.
      """
      if not is_list_like(values):
          raise TypeError(
              "Only list-like objects are allowed to be passed to safe_sort as values"
          )
  
      if not isinstance(values, np.ndarray) and not is_extension_array_dtype(values):
          # don't convert to string types
          dtype, _ = infer_dtype_from_array(values)
          values = np.asarray(values, dtype=dtype)
  
      def sort_mixed(values):
          # order ints before strings, safe in py3
          str_pos = np.array([isinstance(x, str) for x in values], dtype=bool)
          nums = np.sort(values[~str_pos])
          strs = np.sort(values[str_pos])
          return np.concatenate([nums, np.asarray(strs, dtype=object)])
  
      sorter = None
      if (
          not is_extension_array_dtype(values)
          and lib.infer_dtype(values, skipna=False) == "mixed-integer"
      ):
          # unorderable in py3 if mixed str/int
          ordered = sort_mixed(values)
      else:
          try:
              sorter = values.argsort()
              ordered = values.take(sorter)
          except TypeError:
              # try this anyway
              ordered = sort_mixed(values)
  
      # codes:
  
      if codes is None:
          return ordered
  
      if not is_list_like(codes):
          raise TypeError(
              "Only list-like objects or None are allowed to "
              "be passed to safe_sort as codes"
          )
      codes = ensure_platform_int(np.asarray(codes))
  
      if not assume_unique and not len(unique(values)) == len(values):
          raise ValueError("values should be unique if codes is not None")
  
      if sorter is None:
          # mixed types
          hash_klass, values = _get_data_algo(values)
          t = hash_klass(len(values))
          t.map_locations(values)
          sorter = ensure_platform_int(t.lookup(ordered))
  
      if na_sentinel == -1:
          # take_1d is faster, but only works for na_sentinels of -1
          order2 = sorter.argsort()
          new_codes = take_1d(order2, codes, fill_value=-1)
          if verify:
              mask = (codes < -len(values)) | (codes >= len(values))
          else:
              mask = None
      else:
          reverse_indexer = np.empty(len(sorter), dtype=np.int_)
          reverse_indexer.put(sorter, np.arange(len(sorter)))
          # Out of bound indices will be masked with `na_sentinel` next, so we
          # may deal with them here without performance loss using `mode='wrap'`
          new_codes = reverse_indexer.take(codes, mode="wrap")
  
          mask = codes == na_sentinel
          if verify:
              mask = mask | (codes < -len(values)) | (codes >= len(values))
  
      if mask is not None:
          np.putmask(new_codes, mask, na_sentinel)
  
      return ordered, ensure_platform_int(new_codes)
  