conditional_join.py

from __future__ import annotations

import itertools
import math
import operator
from typing import Any, Hashable, Literal, Optional, Union

import numpy as np
import pandas as pd
import pandas_flavor as pf
from pandas.api.types import (
    is_datetime64_dtype,
    is_dtype_equal,
    is_extension_array_dtype,
    is_numeric_dtype,
    is_timedelta64_dtype,
)
from pandas.core.dtypes.concat import concat_compat
from pandas.core.reshape.merge import _MergeOperation

from janitor.functions.utils import (
    _generic_func_cond_join,
    _JoinOperator,
    _keep_output,
    greater_than_join_types,
    less_than_join_types,
)
from janitor.utils import check, check_column


@pf.register_dataframe_method
def conditional_join(
    df: pd.DataFrame,
    right: Union[pd.DataFrame, pd.Series],
    *conditions: Any,
    how: Literal["inner", "left", "right", "outer"] = "inner",
    df_columns: Optional[Any] = slice(None),
    right_columns: Optional[Any] = slice(None),
    keep: Literal["first", "last", "all"] = "all",
    use_numba: bool = False,
    indicator: Optional[Union[bool, str]] = False,
    force: bool = False,
) -> pd.DataFrame:
    """The conditional_join function operates similarly to `pd.merge`,
    but supports joins on inequality operators,
    or a combination of equi and non-equi joins.

    Joins solely on equality are not supported.

    If the join is solely on equality, `pd.merge` function
    covers that; if you are interested in nearest joins, asof joins,
    or rolling joins, then `pd.merge_asof` covers that.
    There is also pandas' IntervalIndex, which is efficient for range joins,
    especially if the intervals do not overlap.

    Column selection in `df_columns` and `right_columns` is possible using the
    [`select`][janitor.functions.select.select] syntax.

    Performance might be improved by setting `use_numba` to `True` -
    this can be handy for equi joins that have lots of duplicated keys.
    This can also be handy for non-equi joins, where there are more than
    two join conditions,
    or there is significant overlap in the range join columns.
    This assumes that `numba` is installed.

    Noticeable performance can be observed for range joins,
    if both join columns from the right dataframe
    are monotonically increasing.

    This function returns rows, if any, where values from `df` meet the
    condition(s) for values from `right`. The conditions are passed in
    as a variable argument of tuples, where the tuple is of
    the form `(left_on, right_on, op)`; `left_on` is the column
    label from `df`, `right_on` is the column label from `right`,
    while `op` is the operator.

    For multiple conditions, the and(`&`)
    operator is used to combine the results of the individual conditions.

    In some scenarios there might be performance gains if the less than join,
    or the greater than join condition, or the range condition
    is executed before the equi join - pass `force=True` to force this.

    The operator can be any of `==`, `!=`, `<=`, `<`, `>=`, `>`.

    There is no optimisation for the `!=` operator.

    The join is done only on the columns.

    For non-equi joins, only numeric, timedelta and date columns are supported.

    `inner`, `left`, `right` and `outer` joins are supported.

    If the columns from `df` and `right` have nothing in common,
    a single index column is returned; else, a MultiIndex column
    is returned.

    Examples:
        >>> import pandas as pd
        >>> import janitor
        >>> df1 = pd.DataFrame({"value_1": [2, 5, 7, 1, 3, 4]})
        >>> df2 = pd.DataFrame({"value_2A": [0, 3, 7, 12, 0, 2, 3, 1],
        ...                     "value_2B": [1, 5, 9, 15, 1, 4, 6, 3],
        ...                    })
        >>> df1
           value_1
        0        2
        1        5
        2        7
        3        1
        4        3
        5        4
        >>> df2
           value_2A  value_2B
        0         0         1
        1         3         5
        2         7         9
        3        12        15
        4         0         1
        5         2         4
        6         3         6
        7         1         3

        >>> df1.conditional_join(
        ...     df2,
        ...     ("value_1", "value_2A", ">"),
        ...     ("value_1", "value_2B", "<")
        ... )
           value_1  value_2A  value_2B
        0        2         1         3
        1        5         3         6
        2        3         2         4
        3        4         3         5
        4        4         3         6

        Select specific columns, after the join:
        >>> df1.conditional_join(
        ...     df2,
        ...     ("value_1", "value_2A", ">"),
        ...     ("value_1", "value_2B", "<"),
        ...     right_columns='value_2B',
        ...     how='left'
        ... )
           value_1  value_2B
        0        2       3.0
        1        5       6.0
        2        3       4.0
        3        4       5.0
        4        4       6.0
        5        7       NaN
        6        1       NaN

        Rename columns, before the join:
        >>> (df1
        ...  .rename(columns={'value_1':'left_column'})
        ...  .conditional_join(
        ...      df2,
        ...     ("left_column", "value_2A", ">"),
        ...     ("left_column", "value_2B", "<"),
        ...      right_columns='value_2B',
        ...      how='outer')
        ... )
            left_column  value_2B
        0           2.0       3.0
        1           5.0       6.0
        2           3.0       4.0
        3           4.0       5.0
        4           4.0       6.0
        5           7.0       NaN
        6           1.0       NaN
        7           NaN       1.0
        8           NaN       9.0
        9           NaN      15.0
        10          NaN       1.0

        Get the first match:
        >>> df1.conditional_join(
        ...     df2,
        ...     ("value_1", "value_2A", ">"),
        ...     ("value_1", "value_2B", "<"),
        ...     keep='first'
        ... )
           value_1  value_2A  value_2B
        0        2         1         3
        1        5         3         6
        2        3         2         4
        3        4         3         5

        Get the last match:
        >>> df1.conditional_join(
        ...     df2,
        ...     ("value_1", "value_2A", ">"),
        ...     ("value_1", "value_2B", "<"),
        ...     keep='last'
        ... )
           value_1  value_2A  value_2B
        0        2         1         3
        1        5         3         6
        2        3         2         4
        3        4         3         6

        Add an indicator column:
        >>> df1.conditional_join(
        ...     df2,
        ...     ("value_1", "value_2A", ">"),
        ...     ("value_1", "value_2B", "<"),
        ...     how='outer',
        ...     indicator=True
        ... )
            value_1  value_2A  value_2B      _merge
        0       2.0       1.0       3.0        both
        1       5.0       3.0       6.0        both
        2       3.0       2.0       4.0        both
        3       4.0       3.0       5.0        both
        4       4.0       3.0       6.0        both
        5       7.0       NaN       NaN   left_only
        6       1.0       NaN       NaN   left_only
        7       NaN       0.0       1.0  right_only
        8       NaN       7.0       9.0  right_only
        9       NaN      12.0      15.0  right_only
        10      NaN       0.0       1.0  right_only

    !!! abstract "Version Changed"

        - 0.24.0
            - Added `df_columns`, `right_columns`, `keep` and `use_numba` parameters.
        - 0.24.1
            - Added `indicator` parameter.
        - 0.25.0
            - `col` class supported.
            - Outer join supported. `sort_by_appearance` deprecated.
            - Numba support for equi join
        - 0.27.0
            - Added support for timedelta dtype.
        - 0.28.0
            - `col` class deprecated.

    Args:
        df: A pandas DataFrame.
        right: Named Series or DataFrame to join to.
        conditions: Variable argument of tuple(s) of the form
            `(left_on, right_on, op)`, where `left_on` is the column
            label from `df`, `right_on` is the column label from `right`,
            while `op` is the operator.
            The `col` class is also supported. The operator can be any of
            `==`, `!=`, `<=`, `<`, `>=`, `>`. For multiple conditions,
            the and(`&`) operator is used to combine the results
            of the individual conditions.
        how: Indicates the type of join to be performed.
            It can be one of `inner`, `left`, `right` or `outer`.
        df_columns: Columns to select from `df` in the final output dataframe.
            Column selection is based on the
            [`select`][janitor.functions.select.select] syntax.
        right_columns: Columns to select from `right` in the final output dataframe.
            Column selection is based on the
            [`select`][janitor.functions.select.select] syntax.
        use_numba: Use numba, if installed, to accelerate the computation.
        keep: Choose whether to return the first match, last match or all matches.
        indicator: If `True`, adds a column to the output DataFrame
            called `_merge` with information on the source of each row.
            The column can be given a different name by providing a string argument.
            The column will have a Categorical type with the value of `left_only`
            for observations whose merge key only appears in the left DataFrame,
            `right_only` for observations whose merge key
            only appears in the right DataFrame, and `both` if the observation’s
            merge key is found in both DataFrames.
        force: If `True`, force the non-equi join conditions to execute before the equi join.


    Returns:
        A pandas DataFrame of the two merged Pandas objects.
    """  # noqa: E501

    return _conditional_join_compute(
        df=df,
        right=right,
        conditions=conditions,
        how=how,
        df_columns=df_columns,
        right_columns=right_columns,
        keep=keep,
        use_numba=use_numba,
        indicator=indicator,
        force=force,
    )


def _check_operator(op: str):
    """
    Check that operator is one of
    `>`, `>=`, `==`, `!=`, `<`, `<=`.

    Used in `conditional_join`.
    """
    sequence_of_operators = {op.value for op in _JoinOperator}
    if op not in sequence_of_operators:
        raise ValueError(
            "The conditional join operator "
            f"should be one of {sequence_of_operators}"
        )


def _conditional_join_preliminary_checks(
    df: pd.DataFrame,
    right: Union[pd.DataFrame, pd.Series],
    conditions: tuple,
    how: str,
    df_columns: Any,
    right_columns: Any,
    keep: str,
    use_numba: bool,
    indicator: Union[bool, str],
    force: bool,
    return_matching_indices: bool = False,
    return_ragged_arrays: bool = False,
) -> tuple:
    """
    Preliminary checks for conditional_join are conducted here.

    Checks include differences in number of column levels,
    length of conditions, existence of columns in dataframe, etc.
    """

    check("right", right, [pd.DataFrame, pd.Series])

    df = df[:]
    right = right[:]

    if isinstance(right, pd.Series):
        if not right.name:
            raise ValueError(
                "Unnamed Series are not supported for conditional_join."
            )
        right = right.to_frame()

    if df.columns.nlevels != right.columns.nlevels:
        raise ValueError(
            "The number of column levels "
            "from the left and right frames must match. "
            "The number of column levels from the left dataframe "
            f"is {df.columns.nlevels}, while the number of column levels "
            f"from the right dataframe is {right.columns.nlevels}."
        )

    if not conditions:
        raise ValueError("Kindly provide at least one join condition.")

    for condition in conditions:
        check("condition", condition, [tuple])
        len_condition = len(condition)
        if len_condition != 3:
            raise ValueError(
                "condition should have only three elements; "
                f"{condition} however is of length {len_condition}."
            )

    for left_on, right_on, op in conditions:
        check("left_on", left_on, [Hashable])
        check("right_on", right_on, [Hashable])
        check("operator", op, [str])
        check_column(df, [left_on])
        check_column(right, [right_on])
        _check_operator(op)

    if (
        all(
            (op == _JoinOperator.STRICTLY_EQUAL.value for *_, op in conditions)
        )
        and not return_matching_indices
    ):
        raise ValueError("Equality only joins are not supported.")

    check("how", how, [str])

    if how not in {"inner", "left", "right", "outer"}:
        raise ValueError(
            "'how' should be one of 'inner', 'left', 'right' or 'outer'."
        )

    if (df.columns.nlevels > 1) and (
        isinstance(df_columns, dict) or isinstance(right_columns, dict)
    ):
        raise ValueError(
            "Column renaming with a dictionary is not supported "
            "for MultiIndex columns."
        )

    check("keep", keep, [str])

    if keep not in {"all", "first", "last"}:
        raise ValueError("'keep' should be one of 'all', 'first', 'last'.")

    check("use_numba", use_numba, [bool])

    check("indicator", indicator, [bool, str])

    check("force", force, [bool])

    check("return_ragged_arrays", return_ragged_arrays, [bool])

    return (
        df,
        right,
        conditions,
        how,
        df_columns,
        right_columns,
        keep,
        use_numba,
        indicator,
        force,
        return_ragged_arrays,
    )


def _conditional_join_type_check(
    left_column: pd.Series, right_column: pd.Series, op: str, use_numba: bool
) -> None:
    """
    Dtype check for columns in the join.
    Checks are not conducted for the equi-join columns,
    except when use_numba is set to True.
    """

    if (
        ((op != _JoinOperator.STRICTLY_EQUAL.value) or use_numba)
        and not is_numeric_dtype(left_column)
        and not is_datetime64_dtype(left_column)
        and not is_timedelta64_dtype(left_column)
    ):
        raise TypeError(
            "Only numeric, timedelta and datetime types "
            "are supported in a non equi-join, "
            "or if use_numba is set to True. "
            f"{left_column.name} in condition "
            f"({left_column.name}, {right_column.name}, {op}) "
            f"has a dtype {left_column.dtype}."
        )

    if (
        (op != _JoinOperator.STRICTLY_EQUAL.value) or use_numba
    ) and not is_dtype_equal(left_column, right_column):
        raise TypeError(
            f"Both columns should have the same type - "
            f"'{left_column.name}' has {left_column.dtype} type;"
            f"'{right_column.name}' has {right_column.dtype} type."
        )

    return None


def _conditional_join_compute(
    df: pd.DataFrame,
    right: pd.DataFrame,
    conditions: list,
    how: str,
    df_columns: Any,
    right_columns: Any,
    keep: str,
    use_numba: bool,
    indicator: Union[bool, str],
    force: bool,
    return_matching_indices: bool = False,
    return_ragged_arrays: bool = False,
) -> pd.DataFrame:
    """
    This is where the actual computation
    for the conditional join takes place.
    """

    (
        df,
        right,
        conditions,
        how,
        df_columns,
        right_columns,
        keep,
        use_numba,
        indicator,
        force,
        return_ragged_arrays,
    ) = _conditional_join_preliminary_checks(
        df=df,
        right=right,
        conditions=conditions,
        how=how,
        df_columns=df_columns,
        right_columns=right_columns,
        keep=keep,
        use_numba=use_numba,
        indicator=indicator,
        force=force,
        return_matching_indices=return_matching_indices,
        return_ragged_arrays=return_ragged_arrays,
    )
    eq_check = False
    le_lt_check = False
    for condition in conditions:
        left_on, right_on, op = condition
        _conditional_join_type_check(
            left_column=df[left_on],
            right_column=right[right_on],
            op=op,
            use_numba=use_numba,
        )
        if op == _JoinOperator.STRICTLY_EQUAL.value:
            eq_check = True
        elif op in less_than_join_types.union(greater_than_join_types):
            le_lt_check = True
    df.index = range(len(df))
    right.index = range(len(right))
    if eq_check:
        result = _multiple_conditional_join_eq(
            df=df,
            right=right,
            conditions=conditions,
            keep=keep,
            use_numba=use_numba,
            force=force,
            return_ragged_arrays=return_ragged_arrays,
        )
    elif (len(conditions) > 1) & le_lt_check:
        result = _multiple_conditional_join_le_lt(
            df=df,
            right=right,
            conditions=conditions,
            keep=keep,
            use_numba=use_numba,
            return_ragged_arrays=return_ragged_arrays,
        )
    elif len(conditions) > 1:
        result = _multiple_conditional_join_ne(
            df=df, right=right, conditions=conditions, keep=keep
        )
    elif use_numba:
        result = _numba_single_non_equi_join(
            left=df[left_on],
            right=right[right_on],
            op=op,
            keep=keep,
        )

    else:
        result = _generic_func_cond_join(
            left=df[left_on],
            right=right[right_on],
            op=op,
            multiple_conditions=False,
            keep=keep,
            return_ragged_arrays=return_ragged_arrays,
        )

    if result is None:
        result = np.array([], dtype=np.intp), np.array([], dtype=np.intp)

    if return_matching_indices:
        return result

    left_index, right_index = result
    return _create_frame(
        df=df,
        right=right,
        left_index=left_index,
        right_index=right_index,
        how=how,
        df_columns=df_columns,
        right_columns=right_columns,
        indicator=indicator,
    )


operator_map = {
    _JoinOperator.STRICTLY_EQUAL.value: operator.eq,
    _JoinOperator.LESS_THAN.value: operator.lt,
    _JoinOperator.LESS_THAN_OR_EQUAL.value: operator.le,
    _JoinOperator.GREATER_THAN.value: operator.gt,
    _JoinOperator.GREATER_THAN_OR_EQUAL.value: operator.ge,
    _JoinOperator.NOT_EQUAL.value: operator.ne,
}


def _generate_indices(
    left_index: np.ndarray,
    right_index: np.ndarray,
    conditions: list[tuple[pd.Series, pd.Series, str]],
) -> tuple:
    """
    Run a for loop to get the final indices.
    This iteratively goes through each condition,
    builds a boolean array,
    and gets indices for rows that meet the condition requirements.
    `conditions` is a list of tuples, where a tuple is of the form:
    `(Series from df, Series from right, operator)`.
    """

    for condition in conditions:
        left, right, op = condition
        left = left._values[left_index]
        right = right._values[right_index]
        op = operator_map[op]
        mask = op(left, right)
        if not mask.any():
            return None
        if is_extension_array_dtype(mask):
            mask = mask.to_numpy(dtype=bool, na_value=False)
        if not mask.all():
            left_index = left_index[mask]
            right_index = right_index[mask]

    return left_index, right_index


def _multiple_conditional_join_ne(
    df: pd.DataFrame,
    right: pd.DataFrame,
    conditions: list[tuple[pd.Series, pd.Series, str]],
    keep: str,
) -> tuple:
    """
    Get indices for multiple conditions,
    where all the operators are `!=`.

    Returns a tuple of (left_index, right_index)
    """
    # currently, there is no optimization option here
    # not equal typically combines less than
    # and greater than, so a lot more rows are returned
    # than just less than or greater than
    first, *rest = conditions
    left_on, right_on, op = first

    indices = _generic_func_cond_join(
        left=df[left_on],
        right=right[right_on],
        op=op,
        multiple_conditions=False,
        keep="all",
    )
    if indices is None:
        return None

    rest = (
        (df[left_on], right[right_on], op) for left_on, right_on, op in rest
    )

    indices = _generate_indices(*indices, rest)

    if not indices:
        return None

    return _keep_output(keep, *indices)


def _multiple_conditional_join_eq(
    df: pd.DataFrame,
    right: pd.DataFrame,
    conditions: list,
    keep: str,
    use_numba: bool,
    force: bool,
    return_ragged_arrays: bool,
) -> tuple:
    """
    Get indices for multiple conditions,
    if any of the conditions has an `==` operator.

    Returns a tuple of (left_index, right_index)
    """

    if force:
        return _multiple_conditional_join_le_lt(
            df=df,
            right=right,
            conditions=conditions,
            keep=keep,
            use_numba=use_numba,
            return_ragged_arrays=False,
        )

    if use_numba:
        eqs = None
        for left_on, right_on, op in conditions:
            if op == _JoinOperator.STRICTLY_EQUAL.value:
                eqs = (left_on, right_on, op)
                break

        le_lt = None
        ge_gt = None

        for condition in conditions:
            *_, op = condition
            if op in less_than_join_types:
                if le_lt:
                    continue
                le_lt = condition
            elif op in greater_than_join_types:
                if ge_gt:
                    continue
                ge_gt = condition
            if le_lt and ge_gt:
                break
        if not le_lt and not ge_gt:
            raise ValueError(
                "At least one less than or greater than "
                "join condition should be present when an equi-join "
                "is present, and use_numba is set to True."
            )
        rest = [
            condition
            for condition in conditions
            if condition not in {eqs, le_lt, ge_gt}
        ]

        right_columns = [eqs[1]]
        df_columns = [eqs[0]]
        # ensure the sort columns are unique
        if ge_gt:
            if ge_gt[1] not in right_columns:
                right_columns.append(ge_gt[1])
            if ge_gt[0] not in df_columns:
                df_columns.append(ge_gt[0])
        if le_lt:
            if le_lt[1] not in right_columns:
                right_columns.append(le_lt[1])
            if le_lt[0] not in df_columns:
                df_columns.append(le_lt[0])

        right_df = right.loc(axis=1)[right_columns]
        left_df = df.loc(axis=1)[df_columns]
        any_nulls = left_df.isna().any(axis=1)
        if any_nulls.all(axis=None):
            return None
        if any_nulls.any():
            left_df = left_df.loc[~any_nulls]
        any_nulls = right_df.isna().any(axis=1)
        if any_nulls.all(axis=None):
            return None
        if any_nulls.any():
            right_df = right.loc[~any_nulls]
        equi_col = right_columns[0]
        # check if the first column is sorted
        # if sorted, check if the second column is sorted
        # per group in the first column
        right_is_sorted = right_df[equi_col].is_monotonic_increasing
        if right_is_sorted:
            grp = right_df.groupby(equi_col, sort=False)
            non_equi_col = right_columns[1]
            # groupby.is_monotonic_increasing uses apply under the hood
            # the approach used below circumvents the Series creation
            # (which isn't required here)
            # and just gets a sequence of booleans, before calling `all`
            # to get a single True or False.
            right_is_sorted = all(
                arr.is_monotonic_increasing for _, arr in grp[non_equi_col]
            )
        if not right_is_sorted:
            right_df = right_df.sort_values(right_columns)
        indices = _numba_equi_join(
            df=left_df, right=right_df, eqs=eqs, ge_gt=ge_gt, le_lt=le_lt
        )
        if indices is None:
            return None
        if not rest:
            return indices

        rest = (
            (df[left_on], right[right_on], op)
            for left_on, right_on, op in rest
        )

        indices = _generate_indices(*indices, rest)

        if indices is None:
            return None

        return _keep_output(keep, *indices)

    if (
        return_ragged_arrays
        & (len(conditions) == 1)
        & (conditions[0][-1] == _JoinOperator.STRICTLY_EQUAL.value)
    ):
        left_on, right_on, op = conditions[0]
        return _generic_func_cond_join(
            left=df[left_on],
            right=right[right_on],
            op=op,
            multiple_conditions=True,
            keep="all",
            return_ragged_arrays=return_ragged_arrays,
        )

    left_df = df[:]
    right_df = right[:]
    eqs = [
        (left_on, right_on)
        for left_on, right_on, op in conditions
        if op == _JoinOperator.STRICTLY_EQUAL.value
    ]

    left_on, right_on = zip(*eqs)
    left_on = list(set(left_on))
    right_on = list(set(right_on))
    any_nulls = left_df.loc[:, left_on].isna().any(axis=1)
    if any_nulls.all():
        return None
    if any_nulls.any():
        left_df = left_df.loc[~any_nulls]
    any_nulls = right_df.loc[:, right_on].isna().any(axis=1)
    if any_nulls.all():
        return None
    if any_nulls.any():
        right_df = right_df.loc[~any_nulls]
    left_on, right_on = zip(*eqs)
    left_on = [*left_on]
    right_on = [*right_on]
    left_index, right_index = _MergeOperation(
        left_df,
        right_df,
        left_on=left_on,
        right_on=right_on,
        sort=False,
    )._get_join_indexers()

    if left_index is not None:
        if not left_index.size:
            return None
        left_index = left_df.index[left_index]
    # patch based on updates in internal code
    # pandas/core/reshape/merge.py#L1692
    # for pandas 2.2
    elif left_index is None:
        left_index = left_df.index._values
    if right_index is not None:
        right_index = right_df.index[right_index]
    else:
        right_index = right_df.index._values

    rest = [
        (df[left_on], right[right_on], op)
        for left_on, right_on, op in conditions
        if op != _JoinOperator.STRICTLY_EQUAL.value
    ]

    if not rest:
        return _keep_output(keep, left_index, right_index)

    indices = _generate_indices(left_index, right_index, rest)
    if indices is None:
        return None

    return _keep_output(keep, *indices)


def _multiple_conditional_join_le_lt(
    df: pd.DataFrame,
    right: pd.DataFrame,
    conditions: list,
    keep: str,
    use_numba: bool,
    return_ragged_arrays: bool,
) -> tuple:
    """
    Get indices for multiple conditions,
    where `>/>=` or `</<=` is present,
    and there is no `==` operator.

    Returns a tuple of (df_index, right_index)
    """
    if use_numba:
        gt_lt = [
            condition
            for condition in conditions
            if condition[-1]
            in less_than_join_types.union(greater_than_join_types)
        ]
        conditions = [
            condition for condition in conditions if condition not in gt_lt
        ]
        if len(gt_lt) > 1:
            first_two = [op for *_, op in gt_lt[:2]]
            range_join_ops = itertools.product(
                less_than_join_types, greater_than_join_types
            )
            range_join_ops = map(set, range_join_ops)
            is_range_join = set(first_two) in range_join_ops
            if is_range_join and (first_two[0] in less_than_join_types):
                gt_lt = [gt_lt[1], gt_lt[0], *gt_lt[2:]]
            if not conditions:
                return _numba_multiple_non_equi_join(
                    df, right, gt_lt, keep=keep, is_range_join=is_range_join
                )
            indices = _numba_multiple_non_equi_join(
                df, right, gt_lt, keep="all", is_range_join=False
            )
        else:
            left_on, right_on, op = gt_lt[0]
            indices = _numba_single_non_equi_join(
                df[left_on], right[right_on], op, keep="all"
            )
        if indices is None:
            return None
    else:
        # there is an opportunity for optimization for range joins
        # which is usually `lower_value < value < upper_value`
        # or `lower_value < a` and `b < upper_value`
        # intervalindex is not used here, as there are scenarios
        # where there will be overlapping intervals;
        # intervalindex does not offer an efficient way to get
        # the indices for overlaps
        # also, intervalindex covers only the first option
        # i.e => `lower_value < value < upper_value`
        # it does not extend to range joins for different columns
        # i.e => `lower_value < a` and `b < upper_value`
        # the option used for range joins is a simple form
        # dependent on sorting and extensible to overlaps
        # as well as the second option:
        # i.e =>`lower_value < a` and `b < upper_value`
        # range joins are also the more common types of non-equi joins
        # the other joins do not have an optimisation opportunity
        # within this space, as far as I know,
        # so a blowup of all the rows is unavoidable.

        # first step is to get two conditions, if possible
        # where one has a less than operator
        # and the other has a greater than operator
        # get the indices from that
        # and then build the remaining indices,
        # using _generate_indices function
        # the aim of this for loop is to see if there is
        # the possibility of a range join, and if there is,
        # then use the optimised path
        first_two = [op for *_, op in conditions[:2]]
        range_join_ops = itertools.product(
            less_than_join_types, greater_than_join_types
        )
        range_join_ops = map(set, range_join_ops)
        is_range_join = set(first_two) in range_join_ops
        # optimised path
        if is_range_join:
            if first_two[0] in less_than_join_types:
                le_lt, ge_gt = conditions[:2]
            else:
                ge_gt, le_lt = conditions[:2]
            conditions = [
                condition
                for condition in conditions
                if condition not in (ge_gt, le_lt)
            ]
            if conditions:
                _keep = None
                return_ragged_arrays = False
                right_is_sorted = False
            else:
                first = ge_gt[1]
                second = le_lt[1]
                right_is_sorted = (
                    right[first].is_monotonic_increasing
                    & right[second].is_monotonic_increasing
                )
                if right_is_sorted:
                    _keep = keep
                else:
                    _keep = None
            indices = _range_indices(
                df=df,
                right=right,
                first=ge_gt,
                second=le_lt,
                keep=_keep,
                return_ragged_arrays=return_ragged_arrays,
                right_is_sorted=right_is_sorted,
            )
            if indices is None:
                return None
            if _keep or (return_ragged_arrays & isinstance(indices[1], list)):
                return indices

        # no optimised path
        # blow up the rows and prune
        else:
            lt_or_gt = None
            for condition in conditions:
                if condition[-1] in less_than_join_types.union(
                    greater_than_join_types
                ):
                    lt_or_gt = condition
                    break
            conditions = [
                condition for condition in conditions if condition != lt_or_gt
            ]
            left_on, right_on, op = lt_or_gt
            indices = _generic_func_cond_join(
                left=df[left_on],
                right=right[right_on],
                op=op,
                multiple_conditions=False,
                keep="all",
            )
    if indices is None:
        return None
    if conditions:
        conditions = (
            (df[left_on], right[right_on], op)
            for left_on, right_on, op in conditions
        )
        indices = _generate_indices(*indices, conditions)
        if indices is None:
            return None
    return _keep_output(keep, *indices)


def _range_indices(
    df: pd.DataFrame,
    right: pd.DataFrame,
    first: tuple,
    second: tuple,
    keep: str,
    right_is_sorted: bool,
    return_ragged_arrays: bool,
) -> Union[tuple[np.ndarray, np.ndarray], None]:
    """
    Retrieve index positions for range/interval joins.

    Idea inspired by article:
    https://www.vertica.com/blog/what-is-a-range-join-and-why-is-it-so-fastba-p223413/

    Returns a tuple of (left_index, right_index)
    """
    # summary of code for range join:
    # get the positions where start_left is >/>= start_right
    # then within the positions,
    # get the positions where end_left is </<= end_right
    # this should reduce the search space
    left_on, right_on, op = first
    left_c = df[left_on]
    right_c = right[right_on]
    left_on, right_on, _ = second
    # get rid of any nulls
    # this is helpful as we can convert extension arrays
    # to numpy arrays safely
    # and simplify the search logic below
    # if there is no fastpath available
    any_nulls = df[left_on].isna()
    if any_nulls.any():
        left_c = left_c[~any_nulls]
    any_nulls = right[right_on].isna()
    if any_nulls.any():
        right_c = right_c[~any_nulls]
    any_nulls = any_nulls.any()

    outcome = _generic_func_cond_join(
        left=left_c,
        right=right_c,
        op=op,
        multiple_conditions=True,
        keep="all",
    )

    if outcome is None:
        return None
    left_index, right_index, ends = outcome
    left_on, right_on, op = second
    left_on = df.columns.get_loc(left_on)
    right_on = right.columns.get_loc(right_on)
    right_c = right.iloc[right_index, right_on]
    left_c = df.iloc[left_index, left_on]
    # if True, we can use a binary search
    # for more performance, instead of a linear search
    fastpath = right_c.is_monotonic_increasing
    if fastpath:
        outcome = _generic_func_cond_join(
            left=left_c,
            right=right_c,
            op=op,
            multiple_conditions=False,
            keep="first",
        )
        if outcome is None:
            return None
        left_c, starts = outcome
    else:
        # the aim here is to get the first match
        # where the left array is </<= than the right array
        # this is solved by getting the cumulative max
        # thus ensuring that the first match is obtained
        # via a binary search
        outcome = _generic_func_cond_join(
            left=left_c,
            right=right_c.cummax(),
            op=op,
            multiple_conditions=True,
            keep="all",
        )
        if outcome is None:
            return None
        left_c, right_index, starts = outcome
    if left_c.size < left_index.size:
        keep_rows = pd.Index(left_c).get_indexer(left_index) != -1
        ends = ends[keep_rows]
        left_index = left_c
    # no point searching within (a, b)
    # if a == b
    # since range(a, b) yields none
    keep_rows = starts < ends

    if not keep_rows.any():
        return None

    if not keep_rows.all():
        left_index = left_index[keep_rows]
        starts = starts[keep_rows]
        ends = ends[keep_rows]

    repeater = ends - starts
    if repeater.max() == 1:
        # no point running a comparison op
        # if the width is all 1
        # this also implies that the intervals
        # do not overlap on the right side
        return left_index, right_index[starts]
    if keep == "first":
        return left_index, right_index[starts]
    if keep == "last":
        return left_index, right_index[ends - 1]
    if return_ragged_arrays & right_is_sorted & fastpath & (not any_nulls):
        right_index = [slice(start, end) for start, end in zip(starts, ends)]
        return left_index, right_index
    right_index = [right_index[start:end] for start, end in zip(starts, ends)]
    if return_ragged_arrays & fastpath:
        return left_index, right_index
    right_index = np.concatenate(right_index)
    left_index = left_index.repeat(repeater)
    if fastpath:
        return left_index, right_index
    # here we search for actual positions
    # where left_c is </<= right_c
    # safe to index the arrays, since we are picking the positions
    # which are all in the original `df` and `right`
    # doing this allows some speed gains
    # while still ensuring correctness
    left_on, right_on, op = second
    left_c = df[left_on]._values[left_index]
    right_c = right[right_on]._values[right_index]
    ext_arr = is_extension_array_dtype(left_c)
    op = operator_map[op]
    mask = op(left_c, right_c)

    if ext_arr:
        mask = mask.to_numpy(dtype=bool, na_value=False)

    if not mask.all():
        left_index = left_index[mask]
        right_index = right_index[mask]

    return left_index, right_index


def _create_multiindex_column(df: pd.DataFrame, right: pd.DataFrame) -> tuple:
    """
    Create a MultiIndex column for conditional_join.
    """
    header = np.empty(df.columns.size, dtype="U4")
    header[:] = "left"
    header = [header]
    columns = [
        df.columns.get_level_values(n) for n in range(df.columns.nlevels)
    ]
    header.extend(columns)
    df.columns = pd.MultiIndex.from_arrays(header)
    header = np.empty(right.columns.size, dtype="U5")
    header[:] = "right"
    header = [header]
    columns = [
        right.columns.get_level_values(n) for n in range(right.columns.nlevels)
    ]
    header.extend(columns)
    right.columns = pd.MultiIndex.from_arrays(header)
    return df, right


def _create_frame(
    df: pd.DataFrame,
    right: pd.DataFrame,
    left_index: np.ndarray,
    right_index: np.ndarray,
    how: str,
    df_columns: Any,
    right_columns: Any,
    indicator: Union[bool, str],
) -> pd.DataFrame:
    """
    Create final dataframe
    """
    if (df_columns is None) and (right_columns is None):
        raise ValueError("df_columns and right_columns cannot both be None.")
    if (df_columns is not None) and (df_columns != slice(None)):
        df = df.select(columns=df_columns)
    if (right_columns is not None) and (right_columns != slice(None)):
        right = right.select(columns=right_columns)
    if df_columns is None:
        df = pd.DataFrame([])
    elif right_columns is None:
        right = pd.DataFrame([])

    if not df.columns.intersection(right.columns).empty:
        df, right = _create_multiindex_column(df, right)

    def _add_indicator(
        indicator: Union[bool, str],
        how: str,
        column_length: int,
        columns: pd.Index,
    ):
        """Adds a categorical column to the DataFrame,
        mapping the rows to either the left or right source DataFrames.

        Args:
            indicator: Indicator column name or True for default name "_merge".
            how: Type of join operation ("inner", "left", "right").
            column_length: Length of the categorical column.
            columns: Columns of the final DataFrame.

        Returns:
            A tuple containing the indicator column name
            and a Categorical array
            representing the indicator values for each row.

        """
        mapping = {"left": "left_only", "right": "right_only", "inner": "both"}
        categories = ["left_only", "right_only", "both"]
        if isinstance(indicator, bool):
            indicator = "_merge"
        if indicator in columns:
            raise ValueError(
                "Cannot use name of an existing column for indicator column"
            )
        nlevels = columns.nlevels
        if nlevels > 1:
            indicator = [indicator] + [""] * (nlevels - 1)
            indicator = tuple(indicator)
        if not column_length:
            arr = pd.Categorical([], categories=categories)
        else:
            arr = pd.Categorical(
                [mapping[how]],
                categories=categories,
            )
            if column_length > 1:
                arr = arr.repeat(column_length)
        return indicator, arr

    def _inner(
        df: pd.DataFrame,
        right: pd.DataFrame,
        left_index: np.ndarray,
        right_index: np.ndarray,
        indicator: Union[bool, str],
    ) -> pd.DataFrame:
        """Computes an inner joined DataFrame.

        Args:
            df: The left DataFrame to join.
            right: The right DataFrame to join.
            left_index: indices from df for rows that match right.
            right_index: indices from right for rows that match df.
            indicator: Indicator column name or True for default name "_merge".

        Returns:
            An inner joined DataFrame.
        """
        dictionary = {}
        for key, value in df.items():
            dictionary[key] = value._values[left_index]
        for key, value in right.items():
            dictionary[key] = value._values[right_index]
        if indicator:
            indicator, arr = _add_indicator(
                indicator=indicator,
                how="inner",
                column_length=left_index.size,
                columns=df.columns.union(right.columns),
            )
            dictionary[indicator] = arr
        return pd.DataFrame(dictionary, copy=False)

    if how == "inner":
        return _inner(
            df=df,
            right=right,
            left_index=left_index,
            right_index=right_index,
            indicator=indicator,
        )
    if how == "left":
        indexer = pd.unique(left_index)
        indexer = pd.Index(indexer).get_indexer(range(len(df)))
        indexer = (indexer < 0).nonzero()[0]
        length = indexer.size
        if not length:
            return _inner(
                df=df,
                right=right,
                left_index=left_index,
                right_index=right_index,
                indicator=indicator,
            )
        dictionary = {}
        for key, value in df.items():
            array = value._values
            top = array[left_index]
            bottom = array[indexer]
            value = concat_compat([top, bottom])
            dictionary[key] = value
        for key, value in right.items():
            array = value._values
            value = array[right_index]
            other = construct_1d_array_from_inferred_fill_value(
                value=array[:1], length=length
            )
            value = concat_compat([value, other])
            dictionary[key] = value
        if indicator:
            columns = df.columns.union(right.columns)
            name, arr1 = _add_indicator(
                indicator=indicator,
                how="inner",
                column_length=right_index.size,
                columns=columns,
            )
            name, arr2 = _add_indicator(
                indicator=indicator,
                how="left",
                column_length=length,
                columns=columns,
            )
            value = concat_compat([arr1, arr2])
            dictionary[name] = value
        return pd.DataFrame(dictionary, copy=False)

    if how == "right":
        indexer = pd.unique(right_index)
        indexer = pd.Index(indexer).get_indexer(range(len(right)))
        indexer = (indexer < 0).nonzero()[0]
        length = indexer.size
        if not length:
            return _inner(
                df=df,
                right=right,
                left_index=left_index,
                right_index=right_index,
                indicator=indicator,
            )
        dictionary = {}
        for key, value in df.items():
            array = value._values
            value = array[left_index]
            other = construct_1d_array_from_inferred_fill_value(
                value=array[:1], length=length
            )
            value = concat_compat([value, other])
            dictionary[key] = value
        for key, value in right.items():
            array = value._values
            top = array[right_index]
            bottom = array[indexer]
            value = concat_compat([top, bottom])
            dictionary[key] = value
        if indicator:
            columns = df.columns.union(right.columns)
            name, arr1 = _add_indicator(
                indicator=indicator,
                how="inner",
                column_length=left_index.size,
                columns=columns,
            )
            name, arr2 = _add_indicator(
                indicator=indicator,
                how="right",
                column_length=length,
                columns=columns,
            )
            value = concat_compat([arr1, arr2])
            dictionary[name] = value
        return pd.DataFrame(dictionary, copy=False)
    # how == 'outer'
    left_indexer = pd.unique(left_index)
    left_indexer = pd.Index(left_indexer).get_indexer(range(len(df)))
    left_indexer = (left_indexer < 0).nonzero()[0]
    right_indexer = pd.unique(right_index)
    right_indexer = pd.Index(right_indexer).get_indexer(range(len(right)))
    right_indexer = (right_indexer < 0).nonzero()[0]

    df_nulls_length = left_indexer.size
    right_nulls_length = right_indexer.size
    dictionary = {}
    for key, value in df.items():
        array = value._values
        top = array[left_index]
        top = [top]
        if df_nulls_length:
            middle = array[left_indexer]
            top.append(middle)
        if right_nulls_length:
            bottom = construct_1d_array_from_inferred_fill_value(
                value=array[:1], length=right_nulls_length
            )
            top.append(bottom)
        if len(top) == 1:
            top = top[0]
        else:
            top = concat_compat(top)
        dictionary[key] = top
    for key, value in right.items():
        array = value._values
        top = array[right_index]
        top = [top]
        if df_nulls_length:
            middle = construct_1d_array_from_inferred_fill_value(
                value=array[:1], length=df_nulls_length
            )
            top.append(middle)
        if right_nulls_length:
            bottom = array[right_indexer]
            top.append(bottom)
        if len(top) == 1:
            top = top[0]
        else:
            top = concat_compat(top)
        dictionary[key] = top
    if indicator:
        columns = df.columns.union(right.columns)
        name, arr1 = _add_indicator(
            indicator=indicator,
            how="inner",
            column_length=right_index.size,
            columns=columns,
        )
        arr1 = [arr1]
        if df_nulls_length:
            name, arr2 = _add_indicator(
                indicator=indicator,
                how="left",
                column_length=df_nulls_length,
                columns=columns,
            )
            arr1.append(arr2)
        if right_nulls_length:
            name, arr3 = _add_indicator(
                indicator=indicator,
                how="right",
                column_length=right_nulls_length,
                columns=columns,
            )
            arr1.append(arr3)
        if len(arr1) == 1:
            arr1 = arr1[0]
        else:
            arr1 = concat_compat(arr1)
        dictionary[name] = arr1

    return pd.DataFrame(dictionary, copy=False)


def get_join_indices(
    df: pd.DataFrame,
    right: Union[pd.DataFrame, pd.Series],
    conditions: list[tuple[str]],
    keep: Literal["first", "last", "all"] = "all",
    use_numba: bool = False,
    force: bool = False,
    return_ragged_arrays: bool = False,
) -> tuple[np.ndarray, np.ndarray]:
    """Convenience function to return the matching indices from an inner join.

    !!! info "New in version 0.27.0"

    !!! abstract "Version Changed"

        - 0.29.0
            - Add support for ragged array indices.

    Args:
        df: A pandas DataFrame.
        right: Named Series or DataFrame to join to.
        conditions: List of arguments of tuple(s) of the form
            `(left_on, right_on, op)`, where `left_on` is the column
            label from `df`, `right_on` is the column label from `right`,
            while `op` is the operator.
            The `col` class is also supported. The operator can be any of
            `==`, `!=`, `<=`, `<`, `>=`, `>`. For multiple conditions,
            the and(`&`) operator is used to combine the results
            of the individual conditions.
        use_numba: Use numba, if installed, to accelerate the computation.
        keep: Choose whether to return the first match, last match or all matches.
        force: If `True`, force the non-equi join conditions
            to execute before the equi join.
        return_ragged_arrays: If `True`, return slices/ranges of matching right indices
            for each matching left index. Not applicable if `use_numba` is `True`.
            If `return_ragged_arrays` is `True`, the join condition
            should be a single join, or a range join,
            where the right columns are both monotonically increasing.

    Returns:
        A tuple of indices for the rows in the dataframes that match.
    """
    return _conditional_join_compute(
        df=df,
        right=right,
        conditions=conditions,
        how="inner",
        df_columns=None,
        right_columns=None,
        keep=keep,
        use_numba=use_numba,
        indicator=False,
        force=force,
        return_matching_indices=True,
        return_ragged_arrays=return_ragged_arrays,
    )


# copied from pandas/core/dtypes/missing.py
# seems function was introduced in 2.2.2
# we should support lesser versions - at least 2.0.0
def construct_1d_array_from_inferred_fill_value(
    value: object, length: int
) -> np.ndarray:
    # Find our empty_value dtype by constructing an array
    #  from our value and doing a .take on it
    from pandas.core.algorithms import take_nd
    from pandas.core.construction import sanitize_array
    from pandas.core.indexes.base import Index

    arr = sanitize_array(value, Index(range(1)), copy=False)
    taker = -1 * np.ones(length, dtype=np.intp)
    return take_nd(arr, taker)


def _numba_single_non_equi_join(
    left: pd.Series, right: pd.Series, op: str, keep: str
) -> tuple[np.ndarray, np.ndarray]:
    """Return matching indices for single non-equi join."""
    if op == "!=":
        return _generic_func_cond_join(
            left=left, right=right, op=op, multiple_conditions=False, keep=keep
        )
    from janitor.functions import _numba

    outcome = _generic_func_cond_join(
        left=left, right=right, op=op, multiple_conditions=True, keep="all"
    )
    if outcome is None:
        return None
    left_index, right_index, starts = outcome
    if op in greater_than_join_types:
        right_index = right_index[::-1]
        starts = right_index.size - starts
    if keep == "first":
        left_indices = np.empty(left_index.size, dtype=np.intp)
        right_indices = np.empty(left_index.size, dtype=np.intp)
        return (
            _numba._numba_non_equi_join_monotonic_increasing_keep_first_dual(
                left_index=left_index,
                right_index=right_index,
                starts=starts,
                left_indices=left_indices,
                right_indices=right_indices,
            )
        )
    if keep == "last":
        left_indices = np.empty(left_index.size, dtype=np.intp)
        right_indices = np.empty(left_index.size, dtype=np.intp)
        return _numba._numba_non_equi_join_monotonic_increasing_keep_last_dual(
            left_index=left_index,
            right_index=right_index,
            starts=starts,
            left_indices=left_indices,
            right_indices=right_indices,
        )
    start_indices = np.empty(left_index.size, dtype=np.intp)
    start_indices[0] = 0
    indices = (right_index.size - starts).cumsum()
    start_indices[1:] = indices[:-1]
    indices = indices[-1]
    left_indices = np.empty(indices, dtype=np.intp)
    right_indices = np.empty(indices, dtype=np.intp)
    return _numba._numba_non_equi_join_monotonic_increasing_keep_all_dual(
        left_index=left_index,
        right_index=right_index,
        starts=starts,
        left_indices=left_indices,
        right_indices=right_indices,
        start_indices=start_indices,
    )


def _numba_multiple_non_equi_join(
    df: pd.DataFrame,
    right: pd.DataFrame,
    gt_lt: list,
    keep: str,
    is_range_join: bool,
) -> tuple[np.ndarray, np.ndarray]:
    """
    # https://www.scitepress.org/papers/2018/68268/68268.pdf
    An alternative to the _range_indices algorithm
    and more generalised - it covers any pair of non equi joins
    in >, >=, <, <=.
    Returns a tuple of left and right indices.
    """
    # implementation is based on the algorithm described in this paper -
    # https://www.scitepress.org/papers/2018/68268/68268.pdf

    # summary:
    # get regions for first and second conditions in the pair
    # (l_col1, r_col1, op1), (l_col2, r_col2, op2)
    # the idea is that r_col1 should always be ahead of the
    # appropriate value from lcol1; same applies to l_col2 & r_col2.
    # if the operator is in less than join types
    # the l_col should be in ascending order
    # if in greater than join types, l_col should be
    # in descending order
    # Example :
    #     df1:
    #    id  value_1
    # 0   1        2
    # 1   1        5
    # 2   1        7
    # 3   2        1
    # 4   2        3
    # 5   3        4
    #
    #
    #  df2:
    #    id  value_2A  value_2B
    # 0   1         0         1
    # 1   1         3         5
    # 2   1         7         9
    # 3   1        12        15
    # 4   2         0         1
    # 5   2         2         4
    # 6   2         3         6
    # 7   3         1         3
    #
    #
    # ('value_1', 'value_2A','>'), ('value_1', 'value_2B', '<')
    # for the first pair, since op is greater than
    # 'value_1' is sorted in descending order
    #  our pairing should be :
    # value  source      region number
    # 12   value_2A       0
    # 7    value_2A       1
    # 7    value_1        2
    # 5    value_1        2
    # 4    value_1        2
    # 3    value_2A       2
    # 3    value_2A       2
    # 3    value_1        3
    # 2    value_2A       3
    # 2    value_1        4
    # 1    value_2A       4
    # 1    value_1        5
    # 0    value_2A       5
    # 0    value_2A       5
    #
    # note that 7 for value_2A is not matched with 7 of value_1
    # because it is >, not >=, hence the different region numbers
    # looking at the output above, we can safely discard regions 0 and 1
    # since they do not have any matches with value_1
    # for the second pair, since op is <, value_1 is sorted
    # in ascending order, and our pairing should be:
    #   value    source    region number
    #     1    value_2B       0
    #     1    value_2B       1
    #     1    value_1        2
    #     2    value_1        2
    #     3    value_2B       2
    #     3    value_1        3
    #     4    value_2B       3
    #     4    value_1        4
    #     5    value_2B       4
    #     5    value_1        5
    #     6    value_2B       5
    #     7    value_1        6
    #     9    value_2B       6
    #     15   value_2B       6
    #
    # from the above we can safely discard regions 0 and 1, since there are
    # no matches with value_1 ... note that the index for regions 0 and 1
    # coincide with the index for region 5 values in value_2A(0, 0);
    # as such those regions will be discarded.
    # Similarly, the index for regions 0 and 1 of value_2A(12, 7)
    # coincide with the index for regions 6 for value_2B(9, 15);
    # these will be discarded as well.
    # let's create a table of the regions, paired with the index
    #
    #
    #  value_1 :
    ###############################################
    # index-->  2  1  5  4  0  3
    # pair1-->  2  2  2  3  4  5
    # pair2-->  6  5  4  3  2  2
    ###############################################
    #
    #
    # value_2A, value_2B
    ##############################################
    # index --> 1  6  5  7
    # pair1 --> 2  2  3  4
    # pair2 --> 4  5  3  2
    ##############################################
    #
    # To find matching indices, the regions from value_1 must be less than
    # or equal to the regions in value_2A/2B.
    # pair1 <= pair1 and pair2 <= pair2
    # Starting from the highest region in value_1
    # 5 in pair1 is not less than any in value_2A/2B, so we discard
    # 4 in pair1 is matched to 4 in pair1 of value_2A/2B
    # we look at the equivalent value in pair2 for 4, which is 2
    # 2 matches 2 in pair 2, so we have a match -> (0, 7)
    # 3 in pair 1 from value_1 matches 3 and 4 in pair1 for value_2A/2B
    # next we compare the equivalent value from pair2, which is 3
    # 3 matches only 3 in value_2A/2B, so our only match is  -> (4, 5)
    # next is 2 (we have 3 2s in value_1 for pair1)
    # they all match 2, 2, 3, 4 in pair1 of value_2A/2B
    # compare the first equivalent in pair2 -> 4
    # 4 matches only 4, 5 in pair2 of value_2A/2B
    # ->(5, 1), (5, 6)
    # the next equivalent is -> 5
    # 5 matches only 5 in pair2 of value_2A/2B
    # -> (1, 6)
    # the last equivalent is -> 6
    # 6 has no match in pair2 of value_2A/2B, so we discard
    # our final matching indices for the left and right pairs
    #########################################################
    # left_index      right_index
    #     0              7
    #     4              5
    #     5              1
    #     5              6
    #     1              6
    ########################################################
    # and if we index the dataframes, we should get the output below:
    #################################
    #    value_1  value_2A  value_2B
    # 0        2         1         3
    # 1        5         3         6
    # 2        3         2         4
    # 3        4         3         5
    # 4        4         3         6
    ################################
    mapping = {">": 0, ">=": 1, "<": 2, "<=": 3}
    first, second, *rest = gt_lt
    if rest:
        left_on, right_on, _ = zip(*rest)
        left_on = list(set(left_on))
        any_nulls = df.loc[:, left_on].isna().any(axis=1)
        if any_nulls.all():
            return None
        if any_nulls.any():
            df = df.loc[~any_nulls]
        right_on = list(set(right_on))
        any_nulls = right.loc[:, right_on].isna().any(axis=1)
        if any_nulls.all():
            return None
        if any_nulls.any():
            right = right.loc[~any_nulls]
    if right[first[1]].is_monotonic_increasing:
        right_is_sorted = True
    else:
        right_is_sorted = False
        right = right.sort_values([first[1], second[1]], ignore_index=False)
    if is_range_join & right[second[1]].is_monotonic_increasing:
        return _range_join_sorted(
            first=first,
            second=second,
            df=df,
            right=right,
            keep=keep,
            gt_lt=gt_lt,
            mapping=mapping,
            rest=rest,
            right_is_sorted=right_is_sorted,
        )

    if not df[first[0]].is_monotonic_increasing:
        df = df.sort_values(first[0], ignore_index=False)
    left_index = df.index._values
    right_index = right.index._values
    l_index = pd.RangeIndex(start=0, stop=left_index.size)
    df.index = l_index
    r_index = pd.RangeIndex(start=0, stop=right_index.size)
    right.index = r_index
    shape = (left_index.size, 2)
    # use the l_booleans and r_booleans
    # to track rows that have complete matches
    left_regions = np.empty(shape=shape, dtype=np.intp, order="F")
    l_booleans = np.zeros(left_index.size, dtype=np.intp)
    shape = (right_index.size, 2)
    right_regions = np.empty(shape=shape, dtype=np.intp, order="F")
    r_booleans = np.zeros(right_index.size, dtype=np.intp)
    for position, (left_column, right_column, op) in enumerate(
        (first, second)
    ):
        outcome = _generic_func_cond_join(
            left=df[left_column],
            right=right[right_column],
            op=op,
            multiple_conditions=True,
            keep="all",
        )
        if outcome is None:
            return None
        left_indexer, right_indexer, search_indices = outcome
        if op in greater_than_join_types:
            search_indices = right_indexer.size - search_indices
            right_indexer = right_indexer[::-1]
        r_region = np.zeros(right_indexer.size, dtype=np.intp)
        r_region[search_indices] = 1
        r_region[0] -= 1
        r_region = r_region.cumsum()
        left_regions[left_indexer, position] = r_region[search_indices]
        l_booleans[left_indexer] += 1
        right_regions[right_indexer, position] = r_region
        r_booleans[right_indexer[search_indices.min() :]] += 1
    r_region = None
    search_indices = None
    booleans = l_booleans == 2
    if not booleans.any():
        return None
    if not booleans.all():
        left_regions = left_regions[booleans]
        left_index = left_index[booleans]
        l_index = l_index[booleans]
    booleans = r_booleans == 2
    if not booleans.any():
        return None
    if not booleans.all():
        right_regions = right_regions[booleans]
        right_index = right_index[booleans]
        r_index = r_index[booleans]
    l_booleans = None
    r_booleans = None
    if gt_lt[0][-1] in greater_than_join_types:
        left_regions = left_regions[::-1]
        left_index = left_index[::-1]
        l_index = l_index[::-1]
        right_regions = right_regions[::-1]
        right_index = right_index[::-1]
        r_index = r_index[::-1]
    starts = right_regions[:, 0].searchsorted(left_regions[:, 0])
    booleans = starts < len(right_regions)
    if not booleans.any():
        return None
    if not booleans.all():
        starts = starts[booleans]
        left_regions = left_regions[booleans]
        left_index = left_index[booleans]
        l_index = l_index[booleans]

    rest = tuple(
        (
            df.loc[l_index, left_on].to_numpy(),
            right.loc[r_index, right_on].to_numpy(),
            mapping[op],
        )
        for left_on, right_on, op in rest
    )

    # a range join will have > and <
    # > and < will be in opposite directions
    # if the first condition is >
    # and the second condition is <
    # and the second condition is monotonic increasing
    # then this kicks in
    if pd.Index(right_regions[:, 1]).is_monotonic_decreasing:
        return _range_join_right_region_monotonic_decreasing(
            left_regions=left_regions,
            right_regions=right_regions,
            left_index=left_index,
            right_index=right_index,
            keep=keep,
            rest=rest,
            starts=starts,
            gt_lt=gt_lt,
            right_is_sorted=right_is_sorted,
        )
    if pd.Index(right_regions[:, 1]).is_monotonic_increasing:
        return _numba_non_equi_join_monotonic_increasing(
            left_regions=left_regions,
            right_regions=right_regions,
            left_index=left_index,
            right_index=right_index,
            keep=keep,
            gt_lt=gt_lt,
            rest=rest,
            starts=starts,
        )
    from janitor.functions import _numba

    # logic here is based on grantjenks' sortedcontainers
    # https://github.com/grantjenks/python-sortedcontainers
    load_factor = 1_000
    width = load_factor * 2
    length = math.ceil(right_index.size / load_factor)
    # maintain a sorted array of the regions
    sorted_array = np.empty(
        (width, length), dtype=right_regions.dtype, order="F"
    )
    # keep track of the positions of each region
    # within the sorted array
    positions_array = np.empty(
        (width, length), dtype=right_regions.dtype, order="F"
    )
    # keep track of the max value per column
    maxxes = np.empty(length, dtype=np.intp)
    # keep track of the length of actual data for each column
    lengths = np.empty(length, dtype=np.intp)
    if (keep == "all") & (len(gt_lt) == 2):
        left_indices, right_indices = (
            _numba._numba_non_equi_join_not_monotonic_dual_keep_all(
                left_regions=left_regions[:, 1],
                right_regions=right_regions[:, 1],
                left_index=left_index,
                right_index=right_index,
                maxxes=maxxes,
                lengths=lengths,
                sorted_array=sorted_array,
                positions_array=positions_array,
                starts=starts,
                load_factor=load_factor,
            )
        )
    elif (keep == "first") & (len(gt_lt) == 2):

        left_indices, right_indices = (
            _numba._numba_non_equi_join_not_monotonic_dual_keep_first(
                left_regions=left_regions[:, 1],
                right_regions=right_regions[:, 1],
                left_index=left_index,
                right_index=right_index,
                maxxes=maxxes,
                lengths=lengths,
                sorted_array=sorted_array,
                positions_array=positions_array,
                starts=starts,
                load_factor=load_factor,
            )
        )
    elif (keep == "last") & (len(gt_lt) == 2):
        left_indices, right_indices = (
            _numba._numba_non_equi_join_not_monotonic_dual_keep_last(
                left_regions=left_regions[:, 1],
                right_regions=right_regions[:, 1],
                left_index=left_index,
                right_index=right_index,
                maxxes=maxxes,
                lengths=lengths,
                sorted_array=sorted_array,
                positions_array=positions_array,
                starts=starts,
                load_factor=load_factor,
            )
        )

    elif keep == "all":
        left_indices, right_indices = (
            _numba._numba_non_equi_join_not_monotonic_keep_all(
                tupled=rest,
                left_index=left_index,
                right_index=right_index,
                left_regions=left_regions[:, 1],
                right_regions=right_regions[:, 1],
                maxxes=maxxes,
                lengths=lengths,
                sorted_array=sorted_array,
                positions_array=positions_array,
                load_factor=load_factor,
                starts=starts,
            )
        )
    elif keep == "first":
        left_indices, right_indices = (
            _numba._numba_non_equi_join_not_monotonic_keep_first(
                tupled=rest,
                left_index=left_index,
                right_index=right_index,
                left_regions=left_regions[:, 1],
                right_regions=right_regions[:, 1],
                maxxes=maxxes,
                lengths=lengths,
                sorted_array=sorted_array,
                positions_array=positions_array,
                load_factor=load_factor,
                starts=starts,
            )
        )
    else:
        left_indices, right_indices = (
            _numba._numba_non_equi_join_not_monotonic_keep_last(
                tupled=rest,
                left_index=left_index,
                right_index=right_index,
                left_regions=left_regions[:, 1],
                right_regions=right_regions[:, 1],
                maxxes=maxxes,
                lengths=lengths,
                sorted_array=sorted_array,
                positions_array=positions_array,
                load_factor=load_factor,
                starts=starts,
            )
        )
    if left_indices is None:
        return None
    return left_indices, right_indices


def _range_join_sorted(
    first: tuple,
    second: tuple,
    df: pd.DataFrame,
    right: pd.DataFrame,
    keep: str,
    gt_lt: tuple,
    mapping: dict,
    rest: list,
    right_is_sorted: bool,
) -> tuple:
    """
    Get indices for a  range join
    if both columns from the right
    are monotonically sorted
    """
    from janitor.functions import _numba

    left_on, right_on, op = first
    outcome = _generic_func_cond_join(
        left=df[left_on],
        right=right[right_on],
        op=op,
        multiple_conditions=True,
        keep="all",
    )
    if not outcome:
        return None
    left_index, right_index, ends = outcome
    left_on, right_on, op = second
    outcome = _generic_func_cond_join(
        left=df.loc[left_index, left_on],
        right=right.loc[right_index, right_on],
        op=op,
        multiple_conditions=True,
        keep="all",
    )
    if outcome is None:
        return None
    left_c, right_index, starts = outcome
    if left_c.size < left_index.size:
        keep_rows = pd.Index(left_c).get_indexer(left_index) != -1
        ends = ends[keep_rows]
        left_index = left_c
    # no point searching within (a, b)
    # if a == b
    # since range(a, b) yields none
    keep_rows = starts < ends
    if not keep_rows.any():
        return None
    if not keep_rows.all():
        left_index = left_index[keep_rows]
        starts = starts[keep_rows]
        ends = ends[keep_rows]
    repeater = ends - starts
    if (len(gt_lt) == 2) & (repeater.max() == 1):
        # no point running a comparison op
        # if the width is all 1
        # this also implies that the intervals
        # do not overlap on the right side
        return left_index, right_index[starts]
    if (len(gt_lt) == 2) & (keep == "first") & right_is_sorted:
        return left_index, right_index[starts]
    if (len(gt_lt) == 2) & (keep == "first"):
        left_indices = np.empty(left_index.size, dtype=np.intp)
        right_indices = np.empty(left_index.size, dtype=np.intp)
        return _numba._numba_range_join_sorted_keep_first_dual(
            left_index=left_index,
            right_index=right_index,
            starts=starts,
            ends=ends,
            left_indices=left_indices,
            right_indices=right_indices,
        )
    if (len(gt_lt) == 2) & (keep == "last") & right_is_sorted:
        return left_index, right_index[ends - 1]
    if (len(gt_lt) == 2) & (keep == "last"):
        left_indices = np.empty(left_index.size, dtype=np.intp)
        right_indices = np.empty(left_index.size, dtype=np.intp)
        return _numba._numba_range_join_sorted_keep_last_dual(
            left_index=left_index,
            right_index=right_index,
            starts=starts,
            ends=ends,
            left_indices=left_indices,
            right_indices=right_indices,
        )
    if (len(gt_lt) == 2) & (keep == "all"):
        start_indices = np.empty(left_index.size, dtype=np.intp)
        start_indices[0] = 0
        indices = (ends - starts).cumsum()
        start_indices[1:] = indices[:-1]
        indices = indices[-1]
        left_indices = np.empty(indices, dtype=np.intp)
        right_indices = np.empty(indices, dtype=np.intp)
        return _numba._range_join_sorted_dual_keep_all(
            left_index=left_index,
            right_index=right_index,
            starts=starts,
            ends=ends,
            left_indices=left_indices,
            right_indices=right_indices,
            start_indices=start_indices,
        )

    rest = tuple(
        (
            df.loc[left_index, left_on].to_numpy(),
            right.loc[right_index, right_on].to_numpy(),
            mapping[op],
        )
        for left_on, right_on, op in rest
    )

    start_indices = np.empty(left_index.size, dtype=np.intp)
    start_indices[0] = 0
    indices = (ends - starts).cumsum()
    start_indices[1:] = indices[:-1]
    indices = indices[-1]
    indices = np.ones(indices, dtype=np.bool_)
    if keep == "all":
        left_indices, right_indices = (
            _numba._range_join_sorted_multiple_keep_all(
                rest,
                left_index=left_index,
                starts=starts,
                ends=ends,
                right_index=right_index,
                indices=indices,
                start_indices=start_indices,
            )
        )
    elif keep == "first":
        left_indices, right_indices = (
            _numba._range_join_sorted_multiple_keep_first(
                rest,
                left_index=left_index,
                starts=starts,
                ends=ends,
                right_index=right_index,
                indices=indices,
                start_indices=start_indices,
            )
        )
    else:
        left_indices, right_indices = (
            _numba._range_join_sorted_multiple_keep_last(
                rest,
                left_index=left_index,
                starts=starts,
                ends=ends,
                right_index=right_index,
                indices=indices,
                start_indices=start_indices,
            )
        )
    if left_indices is None:
        return None
    return left_indices, right_indices


def _range_join_right_region_monotonic_decreasing(
    left_regions: np.ndarray,
    right_regions: np.ndarray,
    left_index: np.ndarray,
    right_index: np.ndarray,
    keep: str,
    gt_lt: tuple,
    rest: tuple,
    starts: np.ndarray,
    right_is_sorted: bool,
):
    """
    Get indices for a range join,
    if the second column in the right region
    is monotonic decreasing
    """
    from janitor.functions import _numba

    ends = right_regions[::-1, 1].searchsorted(left_regions[:, 1])
    ends = len(right_regions) - ends
    booleans = starts < ends
    if not booleans.any():
        return None
    if not booleans.all():
        starts = starts[booleans]
        left_regions = left_regions[booleans]
        left_index = left_index[booleans]
        ends = ends[booleans]
        rest = tuple(
            (left_arr[booleans], right_arr, op)
            for left_arr, right_arr, op in rest
        )
    booleans = None
    if (keep == "first") & (len(gt_lt) == 2) & right_is_sorted:
        return left_index, right_index[ends - 1]
    if (keep == "first") & (len(gt_lt) == 2):
        left_indices = np.empty(left_index.size, dtype=np.intp)
        right_indices = np.empty(left_index.size, dtype=np.intp)
        return _numba._numba_range_join_sorted_keep_first_dual(
            left_index=left_index,
            right_index=right_index,
            starts=starts,
            ends=ends,
            left_indices=left_indices,
            right_indices=right_indices,
        )
    if (keep == "last") & (len(gt_lt) == 2) & right_is_sorted:
        return left_index, right_index[starts]
    if (keep == "last") & (len(gt_lt) == 2):
        left_indices = np.empty(left_index.size, dtype=np.intp)
        right_indices = np.empty(left_index.size, dtype=np.intp)
        return _numba._numba_range_join_sorted_keep_last_dual(
            left_index=left_index,
            right_index=right_index,
            starts=starts,
            ends=ends,
            left_indices=left_indices,
            right_indices=right_indices,
        )
    if (keep == "all") & (len(gt_lt) == 2):
        start_indices = np.empty(left_index.size, dtype=np.intp)
        start_indices[0] = 0
        indices = (ends - starts).cumsum()
        start_indices[1:] = indices[:-1]
        indices = indices[-1]
        left_indices = np.empty(indices, dtype=np.intp)
        right_indices = np.empty(indices, dtype=np.intp)
        return _numba._range_join_sorted_dual_keep_all(
            left_index=left_index,
            right_index=right_index,
            starts=starts,
            ends=ends,
            left_indices=left_indices,
            right_indices=right_indices,
            start_indices=start_indices,
        )
    start_indices = np.empty(left_index.size, dtype=np.intp)
    start_indices[0] = 0
    indices = (ends - starts).cumsum()
    start_indices[1:] = indices[:-1]
    indices = indices[-1]
    indices = np.ones(indices, dtype=np.bool_)
    if keep == "all":
        left_indices, right_indices = (
            _numba._range_join_sorted_multiple_keep_all(
                rest,
                left_index=left_index,
                starts=starts,
                ends=ends,
                right_index=right_index,
                indices=indices,
                start_indices=start_indices,
            )
        )
    elif keep == "first":
        left_indices, right_indices = (
            _numba._range_join_sorted_multiple_keep_first(
                rest,
                left_index=left_index,
                starts=starts,
                ends=ends,
                right_index=right_index,
                indices=indices,
                start_indices=start_indices,
            )
        )

    else:
        left_indices, right_indices = (
            _numba._range_join_sorted_multiple_keep_last(
                rest,
                left_index=left_index,
                starts=starts,
                ends=ends,
                right_index=right_index,
                indices=indices,
                start_indices=start_indices,
            )
        )
    if left_indices is None:
        return None
    return left_indices, right_indices


def _numba_non_equi_join_monotonic_increasing(
    left_regions: np.ndarray,
    right_regions: np.ndarray,
    left_index: np.ndarray,
    right_index: np.ndarray,
    keep: str,
    gt_lt: tuple,
    rest: tuple,
    starts: np.ndarray,
):
    """
    Get indices for a non equi join,
    if the second column in the right region
    is monotonic increasing
    """
    from janitor.functions import _numba

    _starts = right_regions[:, 1].searchsorted(left_regions[:, 1])
    starts = np.where(starts > _starts, starts, _starts)
    booleans = starts == right_index.size
    if booleans.all():
        return None
    if booleans.any():
        booleans = ~booleans
        left_index = left_index[booleans]
        starts = starts[booleans]
        left_regions = left_regions[booleans]
        rest = tuple(
            (left_arr[booleans], right_arr, op)
            for left_arr, right_arr, op in rest
        )
    if (keep == "first") & (len(gt_lt) == 2):
        left_indices = np.empty(left_index.size, dtype=np.intp)
        right_indices = np.empty(left_index.size, dtype=np.intp)
        return (
            _numba._numba_non_equi_join_monotonic_increasing_keep_first_dual(
                left_index=left_index,
                right_index=right_index,
                starts=starts,
                left_indices=left_indices,
                right_indices=right_indices,
            )
        )
    if (keep == "last") & (len(gt_lt) == 2):
        left_indices = np.empty(left_index.size, dtype=np.intp)
        right_indices = np.empty(left_index.size, dtype=np.intp)
        return _numba._numba_non_equi_join_monotonic_increasing_keep_last_dual(
            left_index=left_index,
            right_index=right_index,
            starts=starts,
            left_indices=left_indices,
            right_indices=right_indices,
        )
    if (keep == "all") & (len(gt_lt) == 2):
        start_indices = np.empty(left_index.size, dtype=np.intp)
        start_indices[0] = 0
        indices = (right_index.size - starts).cumsum()
        start_indices[1:] = indices[:-1]
        indices = indices[-1]
        left_indices = np.empty(indices, dtype=np.intp)
        right_indices = np.empty(indices, dtype=np.intp)
        return _numba._numba_non_equi_join_monotonic_increasing_keep_all_dual(
            left_index=left_index,
            right_index=right_index,
            starts=starts,
            left_indices=left_indices,
            right_indices=right_indices,
            start_indices=start_indices,
        )
    start_indices = np.empty(left_index.size, dtype=np.intp)
    start_indices[0] = 0
    indices = (right_index.size - starts).cumsum()
    start_indices[1:] = indices[:-1]
    indices = indices[-1]
    indices = np.ones(indices, dtype=np.bool_)
    if keep == "first":
        left_indices, right_indices = (
            _numba._numba_non_equi_join_monotonic_increasing_keep_first(
                rest,
                left_index=left_index,
                starts=starts,
                right_index=right_index,
                indices=indices,
                start_indices=start_indices,
            )
        )
    elif keep == "last":
        left_indices, right_indices = (
            _numba._numba_non_equi_join_monotonic_increasing_keep_last(
                rest,
                left_index=left_index,
                starts=starts,
                right_index=right_index,
                indices=indices,
                start_indices=start_indices,
            )
        )

    else:
        left_indices, right_indices = (
            _numba._numba_non_equi_join_monotonic_increasing_keep_all(
                rest,
                left_index=left_index,
                starts=starts,
                right_index=right_index,
                indices=indices,
                start_indices=start_indices,
            )
        )
    if left_indices is None:
        return None
    return left_indices, right_indices


def _numba_equi_join(
    df: pd.DataFrame,
    right: pd.DataFrame,
    eqs: tuple,
    ge_gt: tuple,
    le_lt: tuple,
) -> Union[tuple[np.ndarray, np.ndarray], None]:
    """
    Compute indices when an equi join is present.
    """
    # the logic is to delay searching for actual matches
    # while reducing the search space
    # to get the smallest possible search area
    # this serves as an alternative to pandas' hash join
    # and in some cases,
    # usually for many to many joins,
    # can offer significant performance improvements.
    # it relies on binary searches, within the groups,
    # and relies on the fact that sorting ensures the first
    # two columns from the right dataframe are in ascending order
    # per group - this gives us the opportunity to
    # only do a linear search, within the groups,
    # for the last column (if any)
    # (the third column is applicable only for range joins)
    # Example :
    #     df1:
    #    id  value_1
    # 0   1        2
    # 1   1        5
    # 2   1        7
    # 3   2        1
    # 4   2        3
    # 5   3        4
    #
    #
    #  df2:
    #    id  value_2A  value_2B
    # 0   1         0         1
    # 1   1         3         5
    # 2   1         7         9
    # 3   1        12        15
    # 4   2         0         1
    # 5   2         2         4
    # 6   2         3         6
    # 7   3         1         3
    #
    #
    # join condition ->
    # ('id', 'id', '==') &
    # ('value_1', 'value_2A','>') &
    # ('value_1', 'value_2B', '<')
    #
    #
    # note how for df2, id and value_2A
    # are sorted per group
    # the third column (relevant for range join)
    # may or may not be sorted per group
    # (the group is determined by the values of the id column)
    # and as such, we do a linear search in that space, per group
    #
    # first we get the slice boundaries based on id -> ('id', 'id', '==')
    # value     start       end
    #  1         0           4
    #  1         0           4
    #  1         0           4
    #  2         4           7
    #  2         4           7
    #  3         7           8
    #
    # next step is to get the slice end boundaries,
    # based on the greater than condition
    # -> ('value_1', 'value_2A', '>')
    # the search will be within each boundary
    # so for the first row, value_1 is 2
    # the boundary search will be between 0, 4
    # for the last row, value_1 is 4
    # and its boundary search will be between 7, 8
    # since value_2A is sorted per group,
    # a binary search is employed
    # value     start       end      value_1   new_end
    #  1         0           4         2         1
    #  1         0           4         5         2
    #  1         0           4         7         2
    #  2         4           7         1         4
    #  2         4           7         3         6
    #  3         7           8         4         8
    #
    # next step is to get the start boundaries,
    # based on the less than condition
    # -> ('value_1', 'value_2B', '<')
    # note that we have new end boundaries,
    # and as such, our boundaries will use that
    # so for the first row, value_1 is 2
    # the boundary search will be between 0, 1
    # for the 5th row, value_1 is 3
    # and its boundary search will be between 4, 6
    # for value_2B, which is the third column
    # sinc we are not sure whether it is sorted or not,
    # a cumulative max array is used,
    # to get the earliest possible slice start
    # value     start       end      value_1   new_start   new_end
    #  1         0           4         2         -1           1
    #  1         0           4         5         -1           2
    #  1         0           4         7         -1           2
    #  2         4           7         1         -1           5
    #  2         4           7         3         5            6
    #  3         7           8         4         -1           8
    #
    # if there are no matches, boundary is reported as -1
    # from above, we can see that our search space
    # is limited to just 5, 6
    # we can then search for actual matches
    # 	id	value_1	id	value_2A	value_2B
    # 	2	  3	    2	   2	       4
    #
    from janitor.functions import _numba

    left_column, right_column, _ = eqs
    # steal some perf here within the binary search
    # search for uniques
    # and later index them with left_positions
    left_positions, left_arr = df[left_column].factorize(sort=False)
    right_arr = right[right_column]._values
    left_index = df.index._values
    right_index = right.index._values
    slice_starts = right_arr.searchsorted(left_arr, side="left")
    slice_starts = slice_starts[left_positions]
    slice_ends = right_arr.searchsorted(left_arr, side="right")
    slice_ends = slice_ends[left_positions]
    # check if there is a search space
    # this also lets us know if there are equi matches
    keep_rows = slice_starts < slice_ends
    if not keep_rows.any():
        return None
    if not keep_rows.all():
        left_index = left_index[keep_rows]
        slice_starts = slice_starts[keep_rows]
        slice_ends = slice_ends[keep_rows]

    ge_arr1 = None
    ge_arr2 = None
    ge_strict = None
    if ge_gt:
        left_column, right_column, op = ge_gt
        ge_arr1 = df.loc[left_index, left_column]._values
        ge_arr2 = right[right_column]._values
        ge_arr1, ge_arr2 = _convert_to_numpy(left=ge_arr1, right=ge_arr2)
        ge_strict = True if op == ">" else False

    le_arr1 = None
    le_arr2 = None
    le_strict = None
    if le_lt:
        left_column, right_column, op = le_lt
        le_arr1 = df.loc[left_index, left_column]._values
        le_arr2 = right[right_column]._values
        le_arr1, le_arr2 = _convert_to_numpy(left=le_arr1, right=le_arr2)
        le_strict = True if op == "<" else False

    if le_lt and ge_gt:
        group = right.groupby(eqs[1])[le_lt[1]]
        # is the last column (le_lt) monotonic increasing?
        # fast path if it is
        all_monotonic_increasing = all(
            arr.is_monotonic_increasing for _, arr in group
        )
        if all_monotonic_increasing:
            cum_max_arr = le_arr2[:]
        else:
            cum_max_arr = group.cummax()._values
            if is_extension_array_dtype(cum_max_arr):
                array_dtype = cum_max_arr.dtype.numpy_dtype
                cum_max_arr = cum_max_arr.astype(array_dtype)
            if is_datetime64_dtype(cum_max_arr):
                cum_max_arr = cum_max_arr.view(np.int64)

        left_index, right_index = _numba._numba_equi_join_range_join(
            left_index,
            right_index,
            slice_starts,
            slice_ends,
            ge_arr1,
            ge_arr2,
            ge_strict,
            le_arr1,
            le_arr2,
            le_strict,
            all_monotonic_increasing,
            cum_max_arr,
        )

    elif le_lt:
        left_index, right_index = _numba._numba_equi_le_join(
            left_index,
            right_index,
            slice_starts,
            slice_ends,
            le_arr1,
            le_arr2,
            le_strict,
        )

    else:
        left_index, right_index = _numba._numba_equi_ge_join(
            left_index,
            right_index,
            slice_starts,
            slice_ends,
            ge_arr1,
            ge_arr2,
            ge_strict,
        )

    if left_index is None:
        return None

    return left_index, right_index


def _convert_to_numpy(
    left: np.ndarray, right: np.ndarray
) -> tuple[np.ndarray, np.ndarray]:
    """
    Ensure array is a numpy array.
    """
    if is_extension_array_dtype(left):
        array_dtype = left.dtype.numpy_dtype
        left = left.astype(array_dtype)
        right = right.astype(array_dtype)
    if is_datetime64_dtype(left):
        left = left.view(np.int64)
        right = right.view(np.int64)
    return left, right