algorithms.py

"""
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, lib
from pandas._libs.tslib import iNaT
from pandas.util._decorators import Appender, Substitution

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_any_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,
)
from pandas.core.dtypes.generic import ABCIndex, ABCIndexClass, ABCSeries
from pandas.core.dtypes.missing import isna, na_value_for_dtype

import pandas.core.common as com
from pandas.core.construction import array, extract_array
from pandas.core.indexers import validate_indices

if TYPE_CHECKING:
    from pandas import Series

_shared_docs: Dict[str, str] = {}


# --------------- #
# dtype access    #
# --------------- #
def _ensure_data(values, dtype=None):
    """
    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 : str or dtype
    """

    # we check some simple dtypes first
    if is_object_dtype(dtype):
        return ensure_object(np.asarray(values)), "object"
    elif is_object_dtype(values) and dtype is None:
        return ensure_object(np.asarray(values)), "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"), "bool"
        elif is_signed_integer_dtype(values) or is_signed_integer_dtype(dtype):
            return ensure_int64(values), "int64"
        elif is_unsigned_integer_dtype(values) or is_unsigned_integer_dtype(dtype):
            return ensure_uint64(values), "uint64"
        elif is_float_dtype(values) or is_float_dtype(dtype):
            return ensure_float64(values), "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, "float64"

    except (TypeError, ValueError, OverflowError):
        # if we are trying to coerce to a dtype
        # and it is incompat this will fall through to here
        return ensure_object(values), "object"

    # datetimelike
    if (
        needs_i8_conversion(values)
        or is_period_dtype(dtype)
        or is_datetime64_any_dtype(dtype)
        or is_timedelta64_dtype(dtype)
    ):
        if is_period_dtype(values) or is_period_dtype(dtype):
            from pandas import PeriodIndex

            values = PeriodIndex(values)
            dtype = values.dtype
        elif is_timedelta64_dtype(values) 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(values):
                # Avoid calling the DatetimeIndex constructor as it is 1D only
                # Note: this is reached by DataFrame.rank calls GH#27027
                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(values) and (
        is_categorical_dtype(dtype) or dtype is None
    ):
        values = getattr(values, "values", values)
        values = values.codes
        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=np.object)
    return ensure_object(values), "object"


def _reconstruct_data(values, dtype, original):
    """
    reverse of _ensure_data

    Parameters
    ----------
    values : ndarray
    dtype : pandas_dtype
    original : ndarray-like

    Returns
    -------
    Index for extension types, otherwise ndarray casted to dtype
    """

    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:
        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
    Series.unique

    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, values) -> 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, np.ndarray)):
        values = construct_1d_object_array_from_listlike(list(values))

    if is_categorical_dtype(comps):
        # TODO(extension)
        # handle categoricals
        return comps._values.isin(values)

    comps = com.values_from_object(comps)

    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
) -> 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
        Passsed 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.).

    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)

    codes = ensure_platform_int(codes)
    return codes, uniques


_shared_docs[
    "factorize"
] = """
    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)s%(sort)s
    na_sentinel : int, default -1
        Value to mark "not found".
    %(size_hint)s\

    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')
    """


@Substitution(
    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.
    """
    ),
)
@Appender(_shared_docs["factorize"])
def factorize(
    values, sort: bool = False, na_sentinel: int = -1, size_hint: Optional[int] = None
) -> Tuple[np.ndarray, Union[np.ndarray, ABCIndex]]:
    # 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

    if is_extension_array_dtype(values):
        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
        )

    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:
            raise TypeError("bins argument only works with numeric data.")

        # 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


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):
            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 nlargest(self):
        return self.compute("nlargest")

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

    @staticmethod
    def is_valid_dtype_n_method(dtype) -> 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):

        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):

        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)/(nlarrgest: 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

    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._data.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 'algorithms.diff'. In the future this will raise a "
                "TypeError. Convert to a suitable dtype prior to calling 'diff'.",
                FutureWarning,
                stacklevel=stacklevel,
            )
            arr = com.values_from_object(arr)
            dtype = arr.dtype

    is_timedelta = False
    is_bool = False
    if needs_i8_conversion(arr):
        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))

    from pandas import Index

    if not assume_unique and not Index(values).is_unique:
        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)