algorithms.py

"""
Generic data algorithms. This module is experimental at the moment and not
intended for public consumption
"""
from __future__ import annotations

import inspect
import operator
from textwrap import dedent
from typing import (
    TYPE_CHECKING,
    Hashable,
    Literal,
    Sequence,
    cast,
    final,
)
import warnings

import numpy as np

from pandas._libs import (
    algos,
    hashtable as htable,
    iNaT,
    lib,
)
from pandas._typing import (
    AnyArrayLike,
    ArrayLike,
    AxisInt,
    DtypeObj,
    IndexLabel,
    TakeIndexer,
    npt,
)
from pandas.util._decorators import doc
from pandas.util._exceptions import find_stack_level

from pandas.core.dtypes.cast import (
    construct_1d_object_array_from_listlike,
    infer_dtype_from_array,
    sanitize_to_nanoseconds,
)
from pandas.core.dtypes.common import (
    ensure_float64,
    ensure_object,
    ensure_platform_int,
    is_array_like,
    is_bool_dtype,
    is_categorical_dtype,
    is_complex_dtype,
    is_datetime64_dtype,
    is_extension_array_dtype,
    is_float_dtype,
    is_integer,
    is_integer_dtype,
    is_list_like,
    is_numeric_dtype,
    is_object_dtype,
    is_scalar,
    is_signed_integer_dtype,
    is_timedelta64_dtype,
    needs_i8_conversion,
)
from pandas.core.dtypes.concat import concat_compat
from pandas.core.dtypes.dtypes import (
    BaseMaskedDtype,
    ExtensionDtype,
    PandasDtype,
)
from pandas.core.dtypes.generic import (
    ABCDatetimeArray,
    ABCExtensionArray,
    ABCIndex,
    ABCMultiIndex,
    ABCRangeIndex,
    ABCSeries,
    ABCTimedeltaArray,
)
from pandas.core.dtypes.missing import (
    isna,
    na_value_for_dtype,
)

from pandas.core.array_algos.take import take_nd
from pandas.core.construction import (
    array as pd_array,
    ensure_wrapped_if_datetimelike,
    extract_array,
)
from pandas.core.indexers import validate_indices

if TYPE_CHECKING:

    from pandas._typing import (
        NumpySorter,
        NumpyValueArrayLike,
    )

    from pandas import (
        Categorical,
        DataFrame,
        Index,
        MultiIndex,
        Series,
    )
    from pandas.core.arrays import (
        BaseMaskedArray,
        ExtensionArray,
    )


# --------------- #
# dtype access    #
# --------------- #
def _ensure_data(values: ArrayLike) -> np.ndarray:
    """
    routine to ensure that our data is of the correct
    input dtype for lower-level routines

    This will coerce:
    - ints -> int64
    - uint -> uint64
    - bool -> uint8
    - datetimelike -> i8
    - datetime64tz -> i8 (in local tz)
    - categorical -> codes

    Parameters
    ----------
    values : np.ndarray or ExtensionArray

    Returns
    -------
    np.ndarray
    """

    if not isinstance(values, ABCMultiIndex):
        # extract_array would raise
        values = extract_array(values, extract_numpy=True)

    if is_object_dtype(values.dtype):
        return ensure_object(np.asarray(values))

    elif isinstance(values.dtype, BaseMaskedDtype):
        # i.e. BooleanArray, FloatingArray, IntegerArray
        values = cast("BaseMaskedArray", values)
        if not values._hasna:
            # No pd.NAs -> We can avoid an object-dtype cast (and copy) GH#41816
            #  recurse to avoid re-implementing logic for eg bool->uint8
            return _ensure_data(values._data)
        return np.asarray(values)

    elif is_categorical_dtype(values.dtype):
        # NB: cases that go through here should NOT be using _reconstruct_data
        #  on the back-end.
        values = cast("Categorical", values)
        return values.codes

    elif is_bool_dtype(values.dtype):
        if isinstance(values, np.ndarray):
            # i.e. actually dtype == np.dtype("bool")
            return np.asarray(values).view("uint8")
        else:
            # e.g. Sparse[bool, False]  # TODO: no test cases get here
            return np.asarray(values).astype("uint8", copy=False)

    elif is_integer_dtype(values.dtype):
        return np.asarray(values)

    elif is_float_dtype(values.dtype):
        # Note: checking `values.dtype == "float128"` raises on Windows and 32bit
        # error: Item "ExtensionDtype" of "Union[Any, ExtensionDtype, dtype[Any]]"
        # has no attribute "itemsize"
        if values.dtype.itemsize in [2, 12, 16]:  # type: ignore[union-attr]
            # we dont (yet) have float128 hashtable support
            return ensure_float64(values)
        return np.asarray(values)

    elif is_complex_dtype(values.dtype):
        return cast(np.ndarray, values)

    # datetimelike
    elif needs_i8_conversion(values.dtype):
        if isinstance(values, np.ndarray):
            values = sanitize_to_nanoseconds(values)
        npvalues = values.view("i8")
        npvalues = cast(np.ndarray, npvalues)
        return npvalues

    # we have failed, return object
    values = np.asarray(values, dtype=object)
    return ensure_object(values)


def _reconstruct_data(
    values: ArrayLike, dtype: DtypeObj, original: AnyArrayLike
) -> ArrayLike:
    """
    reverse of _ensure_data

    Parameters
    ----------
    values : np.ndarray or ExtensionArray
    dtype : np.dtype or ExtensionDtype
    original : AnyArrayLike

    Returns
    -------
    ExtensionArray or np.ndarray
    """
    if isinstance(values, ABCExtensionArray) and values.dtype == dtype:
        # Catch DatetimeArray/TimedeltaArray
        return values

    if not isinstance(dtype, np.dtype):
        # i.e. ExtensionDtype; note we have ruled out above the possibility
        #  that values.dtype == dtype
        cls = dtype.construct_array_type()

        values = cls._from_sequence(values, dtype=dtype)

    else:
        if is_datetime64_dtype(dtype):
            dtype = np.dtype("datetime64[ns]")
        elif is_timedelta64_dtype(dtype):
            dtype = np.dtype("timedelta64[ns]")

        values = values.astype(dtype, copy=False)

    return values


def _ensure_arraylike(values) -> ArrayLike:
    """
    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", "mixed-integer"]:
            # "mixed-integer" to ensure we do not cast ["ss", 42] to str GH#22160
            if isinstance(values, tuple):
                values = list(values)
            values = construct_1d_object_array_from_listlike(values)
        else:
            values = np.asarray(values)
    return values


_hashtables = {
    "complex128": htable.Complex128HashTable,
    "complex64": htable.Complex64HashTable,
    "float64": htable.Float64HashTable,
    "float32": htable.Float32HashTable,
    "uint64": htable.UInt64HashTable,
    "uint32": htable.UInt32HashTable,
    "uint16": htable.UInt16HashTable,
    "uint8": htable.UInt8HashTable,
    "int64": htable.Int64HashTable,
    "int32": htable.Int32HashTable,
    "int16": htable.Int16HashTable,
    "int8": htable.Int8HashTable,
    "string": htable.StringHashTable,
    "object": htable.PyObjectHashTable,
}


def _get_hashtable_algo(values: np.ndarray):
    """
    Parameters
    ----------
    values : np.ndarray

    Returns
    -------
    htable : HashTable subclass
    values : ndarray
    """
    values = _ensure_data(values)

    ndtype = _check_object_for_strings(values)
    htable = _hashtables[ndtype]
    return htable, values


def _check_object_for_strings(values: np.ndarray) -> str:
    """
    Check if we can use string hashtable instead of object hashtable.

    Parameters
    ----------
    values : ndarray

    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):
    """
    Return unique values based on a hash table.

    Uniques are returned in order of appearance. This does NOT sort.

    Significantly faster than numpy.unique for long enough sequences.
    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"),
    ...         ]
    ...     )
    ... )
    <DatetimeArray>
    ['2016-01-01 00:00:00-05:00']
    Length: 1, dtype: datetime64[ns, US/Eastern]

    >>> 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): ['a', 'b', 'c']

    >>> pd.unique(pd.Series(pd.Categorical(list("baabc"), categories=list("abc"))))
    ['b', 'a', 'c']
    Categories (3, object): ['a', 'b', '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)
    """
    return unique_with_mask(values)


def unique_with_mask(values, mask: npt.NDArray[np.bool_] | None = None):
    """See algorithms.unique for docs. Takes a mask for masked arrays."""
    values = _ensure_arraylike(values)

    if is_extension_array_dtype(values.dtype):
        # Dispatch to extension dtype's unique.
        return values.unique()

    original = values
    htable, values = _get_hashtable_algo(values)

    table = htable(len(values))
    if mask is None:
        uniques = table.unique(values)
        uniques = _reconstruct_data(uniques, original.dtype, original)
        return uniques

    else:
        uniques, mask = table.unique(values, mask=mask)
        uniques = _reconstruct_data(uniques, original.dtype, original)
        assert mask is not None  # for mypy
        return uniques, mask.astype("bool")


unique1d = unique


def isin(comps: AnyArrayLike, values: AnyArrayLike) -> npt.NDArray[np.bool_]:
    """
    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)):
        if not is_signed_integer_dtype(comps):
            # GH#46485 Use object to avoid upcast to float64 later
            # TODO: Share with _find_common_type_compat
            values = construct_1d_object_array_from_listlike(list(values))
        else:
            values = _ensure_arraylike(list(values))
    elif isinstance(values, ABCMultiIndex):
        # Avoid raising in extract_array
        values = np.array(values)
    else:
        values = extract_array(values, extract_numpy=True, extract_range=True)

    comps_array = _ensure_arraylike(comps)
    comps_array = extract_array(comps_array, extract_numpy=True)
    if not isinstance(comps_array, np.ndarray):
        # i.e. Extension Array
        return comps_array.isin(values)

    elif needs_i8_conversion(comps_array.dtype):
        # Dispatch to DatetimeLikeArrayMixin.isin
        return pd_array(comps_array).isin(values)
    elif needs_i8_conversion(values.dtype) and not is_object_dtype(comps_array.dtype):
        # e.g. comps_array are integers and values are datetime64s
        return np.zeros(comps_array.shape, dtype=bool)
        # TODO: not quite right ... Sparse/Categorical
    elif needs_i8_conversion(values.dtype):
        return isin(comps_array, values.astype(object))

    elif isinstance(values.dtype, ExtensionDtype):
        return isin(np.asarray(comps_array), np.asarray(values))

    # GH16012
    # Ensure np.in1d doesn't get object types or it *may* throw an exception
    # Albeit hashmap has O(1) look-up (vs. O(logn) in sorted array),
    # in1d is faster for small sizes
    if (
        len(comps_array) > 1_000_000
        and len(values) <= 26
        and not is_object_dtype(comps_array)
    ):
        # If the values include nan we need to check for nan explicitly
        # since np.nan it not equal to np.nan
        if isna(values).any():

            def f(c, v):
                return np.logical_or(np.in1d(c, v), np.isnan(c))

        else:
            f = np.in1d

    else:
        common = np.find_common_type([values.dtype, comps_array.dtype], [])
        values = values.astype(common, copy=False)
        comps_array = comps_array.astype(common, copy=False)
        f = htable.ismember

    return f(comps_array, values)


def factorize_array(
    values: np.ndarray,
    na_sentinel: int | None = -1,
    size_hint: int | None = None,
    na_value: object = None,
    mask: npt.NDArray[np.bool_] | None = None,
) -> tuple[npt.NDArray[np.intp], np.ndarray]:
    """
    Factorize a numpy array 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[np.intp]
    uniques : ndarray
    """
    ignore_na = na_sentinel is not None
    if not ignore_na:
        na_sentinel = -1

    original = values
    if values.dtype.kind in ["m", "M"]:
        # _get_hashtable_algo will cast dt64/td64 to i8 via _ensure_data, so we
        #  need to do the same to na_value. We are assuming here that the passed
        #  na_value is an appropriately-typed NaT.
        # e.g. test_where_datetimelike_categorical
        na_value = iNaT

    hash_klass, values = _get_hashtable_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,
        ignore_na=ignore_na,
    )

    # re-cast e.g. i8->dt64/td64, uint8->bool
    uniques = _reconstruct_data(uniques, original.dtype, original)

    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: int | None | lib.NoDefault = lib.no_default,
    use_na_sentinel: bool | lib.NoDefault = lib.no_default,
    size_hint: int | None = None,
) -> tuple[np.ndarray, np.ndarray | Index]:
    """
    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.

        .. deprecated:: 1.5.0
            The na_sentinel argument is deprecated and
            will be removed in a future version of pandas. Specify use_na_sentinel as
            either True or False.

        .. versionchanged:: 1.1.2

    use_na_sentinel : bool, default True
        If True, the sentinel -1 will be used for NaN values. If False,
        NaN values will be encoded as non-negative integers and will not drop the
        NaN from the uniques of the values.

        .. versionadded:: 1.5.0
    {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.

    Notes
    -----
    Reference :ref:`the user guide <reshaping.factorize>` for more examples.

    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)

    When ``use_na_sentinel=True`` (the default), missing values are indicated in
    the `codes` with the sentinel value ``-1`` and missing values are not
    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 ``use_na_sentinel=False``.

    >>> values = np.array([1, 2, 1, np.nan])
    >>> codes, uniques = pd.factorize(values)  # default: use_na_sentinel=True
    >>> codes
    array([ 0,  1,  0, -1])
    >>> uniques
    array([1., 2.])

    >>> codes, uniques = pd.factorize(values, use_na_sentinel=False)
    >>> 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.

    # GH#46910 deprecated na_sentinel in favor of use_na_sentinel:
    #   na_sentinel=None corresponds to use_na_sentinel=False
    #   na_sentinel=-1 correspond to use_na_sentinel=True
    # Other na_sentinel values will not be supported when the deprecation is enforced.
    na_sentinel = resolve_na_sentinel(na_sentinel, use_na_sentinel)
    if isinstance(values, ABCRangeIndex):
        return values.factorize(sort=sort)

    values = _ensure_arraylike(values)
    original = values
    if not isinstance(values, ABCMultiIndex):
        values = extract_array(values, extract_numpy=True)

    # 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 = na_sentinel is not None

    if (
        isinstance(values, (ABCDatetimeArray, ABCTimedeltaArray))
        and values.freq is not None
    ):
        # The presence of 'freq' means we can fast-path sorting and know there
        #  aren't NAs
        codes, uniques = values.factorize(sort=sort)
        return _re_wrap_factorize(original, uniques, codes)

    elif not isinstance(values.dtype, np.dtype):
        if (
            na_sentinel == -1 or na_sentinel is None
        ) and "use_na_sentinel" in inspect.signature(values.factorize).parameters:
            # Avoid using catch_warnings when possible
            # GH#46910 - TimelikeOps has deprecated signature
            codes, uniques = values.factorize(  # type: ignore[call-arg]
                use_na_sentinel=na_sentinel is not None
            )
        else:
            na_sentinel_arg = -1 if na_sentinel is None else na_sentinel
            with warnings.catch_warnings():
                # We've already warned above
                warnings.filterwarnings("ignore", ".*use_na_sentinel.*", FutureWarning)
                codes, uniques = values.factorize(na_sentinel=na_sentinel_arg)

    else:
        values = np.asarray(values)  # convert DTA/TDA/MultiIndex
        # TODO: pass na_sentinel=na_sentinel to factorize_array. When sort is True and
        #       na_sentinel is None we append NA on the end because safe_sort does not
        #       handle null values in uniques.
        if na_sentinel is None and sort:
            na_sentinel_arg = -1
        elif na_sentinel is None:
            na_sentinel_arg = None
        else:
            na_sentinel_arg = na_sentinel

        if not dropna and not sort and is_object_dtype(values):
            # factorize can now handle differentiating various types of null values.
            # These can only occur when the array has object dtype.
            # However, for backwards compatibility we only use the null for the
            # provided dtype. This may be revisited in the future, see GH#48476.
            null_mask = isna(values)
            if null_mask.any():
                na_value = na_value_for_dtype(values.dtype, compat=False)
                # Don't modify (potentially user-provided) array
                values = np.where(null_mask, na_value, values)

        codes, uniques = factorize_array(
            values,
            na_sentinel=na_sentinel_arg,
            size_hint=size_hint,
        )

    if sort and len(uniques) > 0:
        if na_sentinel is None:
            # TODO: Can remove when na_sentinel=na_sentinel as in TODO above
            na_sentinel = -1
        uniques, codes = safe_sort(
            uniques, codes, na_sentinel=na_sentinel, assume_unique=True, verify=False
        )

    if not dropna and sort:
        # TODO: Can remove entire block when na_sentinel=na_sentinel as in TODO above
        if na_sentinel is None:
            na_sentinel_arg = -1
        else:
            na_sentinel_arg = na_sentinel
        code_is_na = codes == na_sentinel_arg
        if 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, original.dtype, original)

    return _re_wrap_factorize(original, uniques, codes)


def resolve_na_sentinel(
    na_sentinel: int | None | lib.NoDefault,
    use_na_sentinel: bool | lib.NoDefault,
) -> int | None:
    """
    Determine value of na_sentinel for factorize methods.

    See GH#46910 for details on the deprecation.

    Parameters
    ----------
    na_sentinel : int, None, or lib.no_default
        Value passed to the method.
    use_na_sentinel : bool or lib.no_default
        Value passed to the method.

    Returns
    -------
    Resolved value of na_sentinel.
    """
    if na_sentinel is not lib.no_default and use_na_sentinel is not lib.no_default:
        raise ValueError(
            "Cannot specify both `na_sentinel` and `use_na_sentile`; "
            f"got `na_sentinel={na_sentinel}` and `use_na_sentinel={use_na_sentinel}`"
        )
    if na_sentinel is lib.no_default:
        result = -1 if use_na_sentinel is lib.no_default or use_na_sentinel else None
    else:
        if na_sentinel is None:
            msg = (
                "Specifying `na_sentinel=None` is deprecated, specify "
                "`use_na_sentinel=False` instead."
            )
        elif na_sentinel == -1:
            msg = (
                "Specifying `na_sentinel=-1` is deprecated, specify "
                "`use_na_sentinel=True` instead."
            )
        else:
            msg = (
                "Specifying the specific value to use for `na_sentinel` is "
                "deprecated and will be removed in a future version of pandas. "
                "Specify `use_na_sentinel=True` to use the sentinel value -1, and "
                "`use_na_sentinel=False` to encode NaN values."
            )
        warnings.warn(
            msg, FutureWarning, stacklevel=find_stack_level(inspect.currentframe())
        )
        result = na_sentinel
    return result


def _re_wrap_factorize(original, uniques, codes: np.ndarray):
    """
    Wrap factorize results in Series or Index depending on original type.
    """
    if isinstance(original, ABCIndex):
        uniques = ensure_wrapped_if_datetimelike(uniques)
        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 import (
        Index,
        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:
            values = _ensure_arraylike(values)
            keys, counts = value_counts_arraylike(values, dropna)

            # For backwards compatibility, we let Index do its normal type
            #  inference, _except_ for if if infers from object to bool.
            idx = Index._with_infer(keys)
            if idx.dtype == bool and keys.dtype == object:
                idx = idx.astype(object)

            result = Series(counts, index=idx, name=name)

    if sort:
        result = result.sort_values(ascending=ascending)

    if normalize:
        result = result / counts.sum()

    return result


# Called once from SparseArray, otherwise could be private
def value_counts_arraylike(
    values: np.ndarray, dropna: bool, mask: npt.NDArray[np.bool_] | None = None
) -> tuple[ArrayLike, npt.NDArray[np.int64]]:
    """
    Parameters
    ----------
    values : np.ndarray
    dropna : bool
    mask : np.ndarray[bool] or None, default None

    Returns
    -------
    uniques : np.ndarray
    counts : np.ndarray[np.int64]
    """
    original = values
    values = _ensure_data(values)

    keys, counts = htable.value_count(values, dropna, mask=mask)

    if needs_i8_conversion(original.dtype):
        # datetime, timedelta, or period

        if dropna:
            mask = keys != iNaT
            keys, counts = keys[mask], counts[mask]

    res_keys = _reconstruct_data(keys, original.dtype, original)
    return res_keys, counts


def duplicated(
    values: ArrayLike, keep: Literal["first", "last", False] = "first"
) -> npt.NDArray[np.bool_]:
    """
    Return boolean ndarray denoting duplicate values.

    Parameters
    ----------
    values : nd.array, ExtensionArray or Series
        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[bool]
    """
    if hasattr(values, "dtype") and isinstance(values.dtype, BaseMaskedDtype):
        values = cast("BaseMaskedArray", values)
        return htable.duplicated(values._data, keep=keep, mask=values._mask)

    values = _ensure_data(values)
    return htable.duplicated(values, keep=keep)


def mode(
    values: ArrayLike, dropna: bool = True, mask: npt.NDArray[np.bool_] | None = None
) -> ArrayLike:
    """
    Returns the mode(s) of an array.

    Parameters
    ----------
    values : array-like
        Array over which to check for duplicate values.
    dropna : bool, default True
        Don't consider counts of NaN/NaT.

    Returns
    -------
    np.ndarray or ExtensionArray
    """
    values = _ensure_arraylike(values)
    original = values

    if needs_i8_conversion(values.dtype):
        # Got here with ndarray; dispatch to DatetimeArray/TimedeltaArray.
        values = ensure_wrapped_if_datetimelike(values)
        values = cast("ExtensionArray", values)
        return values._mode(dropna=dropna)

    values = _ensure_data(values)

    npresult = htable.mode(values, dropna=dropna, mask=mask)
    try:
        npresult = np.sort(npresult)
    except TypeError as err:
        warnings.warn(
            f"Unable to sort modes: {err}",
            stacklevel=find_stack_level(inspect.currentframe()),
        )

    result = _reconstruct_data(npresult, original.dtype, original)
    return result


def rank(
    values: ArrayLike,
    axis: AxisInt = 0,
    method: str = "average",
    na_option: str = "keep",
    ascending: bool = True,
    pct: bool = False,
) -> npt.NDArray[np.float64]:
    """
    Rank the values along a given axis.

    Parameters
    ----------
    values : np.ndarray or ExtensionArray
        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 : bool, default True
        Whether or not the elements should be ranked in ascending order.
    pct : bool, 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).
    """
    is_datetimelike = needs_i8_conversion(values.dtype)
    values = _ensure_data(values)

    if values.ndim == 1:
        ranks = algos.rank_1d(
            values,
            is_datetimelike=is_datetimelike,
            ties_method=method,
            ascending=ascending,
            na_option=na_option,
            pct=pct,
        )
    elif values.ndim == 2:
        ranks = algos.rank_2d(
            values,
            axis=axis,
            is_datetimelike=is_datetimelike,
            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: npt.NDArray[np.int64],
    b: int | npt.NDArray[np.int64],
    arr_mask: npt.NDArray[np.bool_] | None = None,
    b_mask: npt.NDArray[np.bool_] | None = None,
) -> npt.NDArray[np.int64]:
    """
    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 : np.ndarray[int64] addend.
    b : array or scalar addend.
    arr_mask : np.ndarray[bool] or None, default None
        array indicating which elements to exclude from checking
    b_mask : np.ndarray[bool] or None, default 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:
        # error: Argument 1 to "__call__" of "_UFunc_Nin1_Nout1" has
        # incompatible type "Optional[ndarray[Any, dtype[bool_]]]";
        # expected "Union[_SupportsArray[dtype[Any]], _NestedSequence
        # [_SupportsArray[dtype[Any]]], bool, int, float, complex, str
        # , bytes, _NestedSequence[Union[bool, int, float, complex, str
        # , bytes]]]"
        not_nan = np.logical_not(b2_mask)  # type: ignore[arg-type]
    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.
    i8max = lib.i8max
    i8min = iNaT

    mask1 = b2 > 0
    mask2 = b2 < 0

    if not mask1.any():
        to_raise = ((i8min - b2 > arr) & not_nan).any()
    elif not mask2.any():
        to_raise = ((i8max - b2 < arr) & not_nan).any()
    else:
        to_raise = ((i8max - b2[mask1] < arr[mask1]) & not_nan[mask1]).any() or (
            (i8min - b2[mask2] > arr[mask2]) & not_nan[mask2]
        ).any()

    if to_raise:
        raise OverflowError("Overflow in int64 addition")

    result = arr + b
    if arr_mask is not None or b2_mask is not None:
        np.putmask(result, ~not_nan, iNaT)

    return result


# --------------- #
# select n        #
# --------------- #


class SelectN:
    def __init__(self, obj, n: int, keep: str) -> None:
        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) -> DataFrame | Series:
        raise NotImplementedError

    @final
    def nlargest(self):
        return self.compute("nlargest")

    @final
    def nsmallest(self):
        return self.compute("nsmallest")

    @final
    @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:

        from pandas.core.reshape.concat import concat

        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()
        nan_index = self.obj.drop(dropped.index)

        # slow method
        if n >= len(self.obj):
            ascending = method == "nsmallest"
            return self.obj.sort_values(ascending=ascending).head(n)

        # fast method
        new_dtype = dropped.dtype
        arr = _ensure_data(dropped.values)
        if method == "nlargest":
            arr = -arr
            if is_integer_dtype(new_dtype):
                # GH 21426: ensure reverse ordering at boundaries
                arr -= 1

            elif is_bool_dtype(new_dtype):
                # GH 26154: ensure False is smaller than True
                arr = 1 - (-arr)

        if self.keep == "last":
            arr = arr[::-1]

        nbase = n
        narr = len(arr)
        n = min(n, narr)

        # arr passed into kth_smallest must be contiguous. We copy
        # here because kth_smallest will modify its input
        kth_val = algos.kth_smallest(arr.copy(order="C"), n - 1)
        (ns,) = np.nonzero(arr <= kth_val)
        inds = ns[arr[ns].argsort(kind="mergesort")]

        if self.keep != "all":
            inds = inds[:n]
            findex = nbase
        else:
            if len(inds) < nbase and len(nan_index) + len(inds) >= nbase:
                findex = len(nan_index) + len(inds)
            else:
                findex = len(inds)

        if self.keep == "last":
            # reverse indices
            inds = narr - 1 - inds

        return concat([dropped.iloc[inds], nan_index]).iloc[:findex]


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: DataFrame, n: int, keep: str, columns: IndexLabel) -> None:
        super().__init__(obj, n, keep)
        if not is_list_like(columns) or isinstance(columns, tuple):
            columns = [columns]

        columns = cast(Sequence[Hashable], columns)
        columns = list(columns)
        self.columns = columns

    def compute(self, method: str) -> DataFrame:

        from pandas.core.api 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 take(
    arr,
    indices: TakeIndexer,
    axis: AxisInt = 0,
    allow_fill: bool = False,
    fill_value=None,
):
    """
    Take elements from an array.

    Parameters
    ----------
    arr : array-like or scalar value
        Non array-likes (sequences/scalars without a dtype) are coerced
        to an ndarray.
    indices : sequence of int or one-dimensional np.ndarray of int
        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
          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
    --------
    >>> import pandas as pd

    With the default ``allow_fill=False``, negative numbers indicate
    positional indices from the right.

    >>> pd.api.extensions.take(np.array([10, 20, 30]), [0, 0, -1])
    array([10, 10, 30])

    Setting ``allow_fill=True`` will place `fill_value` in those positions.

    >>> pd.api.extensions.take(np.array([10, 20, 30]), [0, 0, -1], allow_fill=True)
    array([10., 10., nan])

    >>> pd.api.extensions.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_nd(
            arr, indices, axis=axis, allow_fill=True, fill_value=fill_value
        )
    else:
        # NumPy style
        result = arr.take(indices, axis=axis)
    return result


# ------------ #
# searchsorted #
# ------------ #


def searchsorted(
    arr: ArrayLike,
    value: NumpyValueArrayLike | ExtensionArray,
    side: Literal["left", "right"] = "left",
    sorter: NumpySorter = None,
) -> npt.NDArray[np.intp] | np.intp:
    """
    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: np.ndarray, ExtensionArray, Series
        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 or scalar
        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 or int
        If value is array-like, array of insertion points.
        If value is scalar, a single integer.

    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.dtype)
        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):
            # We know that value is int
            value = cast(int, dtype.type(value))
        else:
            value = pd_array(cast(ArrayLike, value), dtype=dtype)
    else:
        # E.g. if `arr` is an array with dtype='datetime64[ns]'
        # and `value` is a pd.Timestamp, we may need to convert value
        arr = ensure_wrapped_if_datetimelike(arr)

    # Argument 1 to "searchsorted" of "ndarray" has incompatible type
    # "Union[NumpyValueArrayLike, ExtensionArray]"; expected "NumpyValueArrayLike"
    return arr.searchsorted(value, side=side, sorter=sorter)  # type: ignore[arg-type]


# ---- #
# diff #
# ---- #

_diff_special = {"float64", "float32", "int64", "int32", "int16", "int8"}


def diff(arr, n: int, axis: AxisInt = 0):
    """
    difference of n between self,
    analogous to s-s.shift(n)

    Parameters
    ----------
    arr : ndarray or ExtensionArray
    n : int
        number of periods
    axis : {0, 1}
        axis to shift on
    stacklevel : int, default 3
        The stacklevel for the lost dtype warning.

    Returns
    -------
    shifted
    """

    n = int(n)
    na = np.nan
    dtype = arr.dtype

    is_bool = is_bool_dtype(dtype)
    if is_bool:
        op = operator.xor
    else:
        op = operator.sub

    if isinstance(dtype, PandasDtype):
        # PandasArray cannot necessarily hold shifted versions of itself.
        arr = arr.to_numpy()
        dtype = arr.dtype

    if not isinstance(dtype, np.dtype):
        # i.e ExtensionDtype
        if hasattr(arr, f"__{op.__name__}__"):
            if axis != 0:
                raise ValueError(f"cannot diff {type(arr).__name__} on axis={axis}")
            return op(arr, arr.shift(n))
        else:
            warnings.warn(
                "dtype lost in 'diff()'. In the future this will raise a "
                "TypeError. Convert to a suitable dtype prior to calling 'diff'.",
                FutureWarning,
                stacklevel=find_stack_level(inspect.currentframe()),
            )
            arr = np.asarray(arr)
            dtype = arr.dtype

    is_timedelta = False
    if needs_i8_conversion(arr.dtype):
        dtype = np.int64
        arr = arr.view("i8")
        na = iNaT
        is_timedelta = True

    elif is_bool:
        # We have to cast in order to be able to hold np.nan
        dtype = np.object_

    elif is_integer_dtype(dtype):
        # We have to cast in order to be able to hold np.nan

        # int8, int16 are incompatible with float64,
        # see https://github.com/cython/cython/issues/2646
        if arr.dtype.name in ["int8", "int16"]:
            dtype = np.float32
        else:
            dtype = np.float64

    orig_ndim = arr.ndim
    if orig_ndim == 1:
        # reshape so we can always use algos.diff_2d
        arr = arr.reshape(-1, 1)
        # TODO: require axis == 0

    dtype = np.dtype(dtype)
    out_arr = np.empty(arr.shape, dtype=dtype)

    na_indexer = [slice(None)] * 2
    na_indexer[axis] = slice(None, n) if n >= 0 else slice(n, None)
    out_arr[tuple(na_indexer)] = na

    if 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, datetimelike=is_timedelta)
    else:
        # To keep mypy happy, _res_indexer is a list while res_indexer is
        #  a tuple, ditto for lag_indexer.
        _res_indexer = [slice(None)] * 2
        _res_indexer[axis] = slice(n, None) if n >= 0 else slice(None, n)
        res_indexer = tuple(_res_indexer)

        _lag_indexer = [slice(None)] * 2
        _lag_indexer[axis] = slice(None, -n) if n > 0 else slice(-n, None)
        lag_indexer = tuple(_lag_indexer)

        out_arr[res_indexer] = op(arr[res_indexer], arr[lag_indexer])

    if is_timedelta:
        out_arr = out_arr.view("timedelta64[ns]")

    if orig_ndim == 1:
        out_arr = out_arr[:, 0]
    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,
) -> np.ndarray | MultiIndex | tuple[np.ndarray | MultiIndex, 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 or MultiIndex
        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, ABCExtensionArray, ABCMultiIndex)):
        # don't convert to string types
        dtype, _ = infer_dtype_from_array(values)
        # error: Argument "dtype" to "asarray" has incompatible type "Union[dtype[Any],
        # ExtensionDtype]"; expected "Union[dtype[Any], None, type, _SupportsDType, str,
        # Union[Tuple[Any, int], Tuple[Any, Union[int, Sequence[int]]], List[Any],
        # _DTypeDict, Tuple[Any, Any]]]"
        values = np.asarray(values, dtype=dtype)  # type: ignore[arg-type]

    sorter = None
    ordered: np.ndarray | MultiIndex

    if (
        not is_extension_array_dtype(values)
        and lib.infer_dtype(values, skipna=False) == "mixed-integer"
    ):
        ordered = _sort_mixed(values)
    else:
        try:
            sorter = values.argsort()
            ordered = values.take(sorter)
        except TypeError:
            # Previous sorters failed or were not applicable, try `_sort_mixed`
            # which would work, but which fails for special case of 1d arrays
            # with tuples.
            if values.size and isinstance(values[0], tuple):
                ordered = _sort_tuples(values)
            else:
                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_hashtable_algo(values)
        t = hash_klass(len(values))
        t.map_locations(values)
        sorter = ensure_platform_int(t.lookup(ordered))

    if na_sentinel == -1:
        # take_nd is faster, but only works for na_sentinels of -1
        order2 = sorter.argsort()
        new_codes = take_nd(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)


def _sort_mixed(values) -> np.ndarray:
    """order ints before strings in 1d arrays, safe in py3"""
    str_pos = np.array([isinstance(x, str) for x in values], dtype=bool)
    none_pos = np.array([x is None for x in values], dtype=bool)
    nums = np.sort(values[~str_pos & ~none_pos])
    strs = np.sort(values[str_pos])
    return np.concatenate(
        [nums, np.asarray(strs, dtype=object), np.array(values[none_pos])]
    )


def _sort_tuples(values: np.ndarray) -> np.ndarray:
    """
    Convert array of tuples (1d) to array of arrays (2d).
    We need to keep the columns separately as they contain different types and
    nans (can't use `np.sort` as it may fail when str and nan are mixed in a
    column as types cannot be compared).
    """
    from pandas.core.internals.construction import to_arrays
    from pandas.core.sorting import lexsort_indexer

    arrays, _ = to_arrays(values, None)
    indexer = lexsort_indexer(arrays, orders=True)
    return values[indexer]


def union_with_duplicates(
    lvals: ArrayLike | Index, rvals: ArrayLike | Index
) -> ArrayLike | Index:
    """
    Extracts the union from lvals and rvals with respect to duplicates and nans in
    both arrays.

    Parameters
    ----------
    lvals: np.ndarray or ExtensionArray
        left values which is ordered in front.
    rvals: np.ndarray or ExtensionArray
        right values ordered after lvals.

    Returns
    -------
    np.ndarray or ExtensionArray
        Containing the unsorted union of both arrays.

    Notes
    -----
    Caller is responsible for ensuring lvals.dtype == rvals.dtype.
    """
    from pandas import Series

    l_count = value_counts(lvals, dropna=False)
    r_count = value_counts(rvals, dropna=False)
    l_count, r_count = l_count.align(r_count, fill_value=0)
    final_count = np.maximum(l_count.values, r_count.values)
    final_count = Series(final_count, index=l_count.index, dtype="int", copy=False)
    if isinstance(lvals, ABCMultiIndex) and isinstance(rvals, ABCMultiIndex):
        unique_vals = lvals.append(rvals).unique()
    else:
        if isinstance(lvals, ABCIndex):
            lvals = lvals._values
        if isinstance(rvals, ABCIndex):
            rvals = rvals._values
        unique_vals = unique(concat_compat([lvals, rvals]))
        unique_vals = ensure_wrapped_if_datetimelike(unique_vals)
    repeats = final_count.reindex(unique_vals).values
    return np.repeat(unique_vals, repeats)