Add API specifications for returning the k largest elements

Ref: #629
Ref: numpy/numpy#19117
Ref: numpy/numpy#15128
Ref: https://mail.python.org/archives/list/numpy-discussion@python.org/thread/F4P5UVTAKRJJ3OORI6UOWFSUEE5CNTSC/#PELUDW5ACUBHBNK5IVGWIWTQHBM2HXUP

spec/draft/API_specification/searching_functions.rst

@@ -23,4 +23,7 @@ Objects in API
    argmax
    argmin
    nonzero
+   top_k
+   top_k_indices
+   top_k_values
    where

src/array_api_stubs/_draft/searching_functions.py

@@ -1,7 +1,15 @@
-__all__ = ["argmax", "argmin", "nonzero", "where"]
+__all__ = [
+    "argmax",
+    "argmin",
+    "nonzero",
+    "top_k",
+    "top_k_values",
+    "top_k_indices",
+    "where",
+]
 
 
-from ._types import Optional, Tuple, array
+from ._types import Optional, Literal, Tuple, array
 
 
 def argmax(x: array, /, *, axis: Optional[int] = None, keepdims: bool = False) -> array:
@@ -87,6 +95,126 @@ def nonzero(x: array, /) -> Tuple[array, ...]:
     """
 
 
+def top_k(
+    x: array,
+    k: int,
+    /,
+    *,
+    axis: Optional[int] = None,
+    mode: Literal["largest", "smallest"] = "largest",
+) -> Tuple[array, array]:
+    """
+    Returns the ``k`` largest (or smallest) elements of an input array ``x`` along a specified dimension.
+
+    Parameters
+    ----------
+    x: array
+        input array. Should have a real-valued data type.
+    k: int
+        number of elements to find. Must be a positive integer value.
+    axis: Optional[int]
+        axis along which to search. If ``None``, the function must search the flattened array. Default: ``None``.
+    mode: Literal['largest', 'smallest']
+        search mode. Must be one of the following modes:
+
+        -  ``'largest'``: return the ``k`` largest elements.
+        -  ``'smallest'``: return the ``k`` smallest elements.
+
+    Returns
+    -------
+    out: Tuple[array, array]
+        a namedtuple ``(values, indices)`` whose
+
+        - first element must have the field name ``values`` and must be an array containing the ``k`` largest (or smallest) elements of ``x``. The array must have the same data type as ``x``. If ``axis`` is ``None``, the array must be a one-dimensional array having shape ``(k,)``; otherwise, if ``axis`` is an integer value, the array must have the same rank (number of dimensions) and shape as ``x``, except for the axis specified by ``axis`` which must have size ``k``.
+        - second element must have the field name ``indices`` and must be an array containing indices of ``x`` that result in ``values``. The array must have the same shape as ``values`` and must have the default array index data type. If ``axis`` is ``None``, ``indices`` must be the indices of a flattened ``x``.
+
+    Notes
+    -----
+
+    -   If ``k`` exceeds the number of elements in ``x`` or along the axis specified by ``axis``, behavior is left unspecified and thus implementation-dependent. Conforming implementations may choose, e.g., to raise an exception or return all elements.
+    -   The order of the returned values and indices is left unspecified and thus implementation-dependent. Conforming implementations may return sorted or unsorted values.
+    -   Conforming implementations may support complex numbers; however, inequality comparison of complex numbers is unspecified and thus implementation-dependent (see :ref:`complex-number-ordering`).
+    """
+
+
+def top_k_indices(
+    x: array,
+    k: int,
+    /,
+    *,
+    axis: Optional[int] = None,
+    mode: Literal["largest", "smallest"] = "largest",
+) -> array:
+    """
+    Returns the indices of the ``k`` largest (or smallest) elements of an input array ``x`` along a specified dimension.
+
+    Parameters
+    ----------
+    x: array
+        input array. Should have a real-valued data type.
+    k: int
+        number of elements to find. Must be a positive integer value.
+    axis: Optional[int]
+        axis along which to search. If ``None``, the function must search the flattened array. Default: ``None``.
+    mode: Literal['largest', 'smallest']
+        search mode. Must be one of the following modes:
+
+        -  ``'largest'``: return the indices of the ``k`` largest elements.
+        -  ``'smallest'``: return the indices of the ``k`` smallest elements.
+
+    Returns
+    -------
+    out: array
+        an array containing indices corresponding to the ``k`` largest (or smallest) elements of ``x``. The array must have the default array index data type.  If ``axis`` is ``None``, the array must be a one-dimensional array having shape ``(k,)`` and contain the indices of a flattened ``x``; otherwise, if ``axis`` is an integer value, the array must have the same rank (number of dimensions) and shape as ``x``, except for the axis specified by ``axis`` which must have size ``k``.
+
+    Notes
+    -----
+
+    -   If ``k`` exceeds the number of elements in ``x`` or along the axis specified by ``axis``, behavior is left unspecified and thus implementation-dependent. Conforming implementations may choose, e.g., to raise an exception or return all indices.
+    -   The order of the returned indices is left unspecified and thus implementation-dependent. Conforming implementations may return indices corresponding to sorted or unsorted values.
+    -   Conforming implementations may support complex numbers; however, inequality comparison of complex numbers is unspecified and thus implementation-dependent (see :ref:`complex-number-ordering`).
+    """
+
+
+def top_k_values(
+    x: array,
+    k: int,
+    /,
+    *,
+    axis: Optional[int] = None,
+    mode: Literal["largest", "smallest"] = "largest",
+) -> array:
+    """
+    Returns the ``k`` largest (or smallest) elements of an input array ``x`` along a specified dimension.
+
+    Parameters
+    ----------
+    x: array
+        input array. Should have a real-valued data type.
+    k: int
+        number of elements to find. Must be a positive integer value.
+    axis: Optional[int]
+        axis along which to search. If ``None``, the function must search the flattened array. Default: ``None``.
+    mode: Literal['largest', 'smallest']
+        search mode. Must be one of the following modes:
+
+        -  ``'largest'``: return the indices of the ``k`` largest elements.
+        -  ``'smallest'``: return the indices of the ``k`` smallest elements.
+
+    Returns
+    -------
+    out: array
+        an array containing the ``k`` largest (or smallest) elements of ``x``. The array must have the same data type as ``x``.  If ``axis`` is ``None``, the array must be a one-dimensional array having shape ``(k,)``; otherwise, if ``axis`` is an integer value, the array must have the same rank (number of dimensions) and shape as ``x``, except for the axis specified by ``axis`` which must have size ``k``.
+
+    Notes
+    -----
+
+    -   If ``k`` exceeds the number of elements in ``x`` or along the axis specified by ``axis``, behavior is left unspecified and thus implementation-dependent. Conforming implementations may choose, e.g., to raise an exception or return all indices.
+    -   The order of the returned values is left unspecified and thus implementation-dependent. Conforming implementations may return sorted or unsorted values.
+    -   Conforming implementations may support complex numbers; however, inequality comparison of complex numbers is unspecified and thus implementation-dependent (see :ref:`complex-number-ordering`).
+    """
+
+
 def where(condition: array, x1: array, x2: array, /) -> array:
     """
     Returns elements chosen from ``x1`` or ``x2`` depending on ``condition``.