diff --git a/spec/API_specification/array_api/array_object.py b/spec/API_specification/array_api/array_object.py
index 94dac2d1d..dd70a1beb 100644
--- a/spec/API_specification/array_api/array_object.py
+++ b/spec/API_specification/array_api/array_object.py
@@ -224,12 +224,22 @@ def __array_namespace__(self: array, /, *, api_version: Optional[str] = None) ->
def __bool__(self: array, /) -> bool:
"""
- Converts a zero-dimensional boolean array to a Python ``bool`` object.
+ Converts a zero-dimensional array to a Python ``bool`` object.
+
+ **Special cases**
+
+ For real-valued floating-point operands,
+
+ - If ``self`` is ``NaN``, the result is ``True``.
+ - If ``self`` is either ``+infinity`` or ``-infinity``, the result is ``True``.
+ - If ``self`` is either ``+0`` or ``-0``, the result is ``False``.
+
+ For complex floating-point operands, special cases must be handled as if the operation is implemented as the logical AND of ``bool(real(self))`` and ``bool(imag(self))``.
Parameters
----------
self: array
- zero-dimensional array instance. Must have a boolean data type.
+ zero-dimensional array instance.
Returns
-------
@@ -237,6 +247,35 @@ def __bool__(self: array, /) -> bool:
a Python ``bool`` object representing the single element of the array.
"""
+ def __complex__(self: array, /) -> complex:
+ """
+ Converts a zero-dimensional array to a Python ``complex`` object.
+
+ **Special cases**
+
+ For boolean operands,
+
+ - If ``self`` is ``True``, the result is ``1+0j``.
+ - If ``self`` is ``False``, the result is ``0+0j``.
+
+ For real-valued floating-point operands,
+
+ - If ``self`` is ``NaN``, the result is ``NaN + NaN j``.
+ - If ``self`` is ``+infinity``, the result is ``+infinity + 0j``.
+ - If ``self`` is ``-infinity``, the result is ``-infinity + 0j``.
+ - If ``self`` is a finite number, the result is ``self + 0j``.
+
+ Parameters
+ ----------
+ self: array
+ zero-dimensional array instance.
+
+ Returns
+ -------
+ out: complex
+ a Python ``complex`` object representing the single element of the array instance.
+ """
+
def __dlpack__(self: array, /, *, stream: Optional[Union[int, Any]] = None) -> PyCapsule:
"""
Exports the array for consumption by :func:`~array_api.from_dlpack` as a DLPack capsule.
@@ -341,12 +380,22 @@ def __eq__(self: array, other: Union[int, float, bool, array], /) -> array:
def __float__(self: array, /) -> float:
"""
- Converts a zero-dimensional floating-point array to a Python ``float`` object.
+ Converts a zero-dimensional array to a Python ``float`` object.
+
+ .. note::
+ Casting integer values outside the representable bounds of Python's float type is not specified and is implementation-dependent.
+
+ **Special cases**
+
+ For boolean operands,
+
+ - If ``self`` is ``True``, the result is ``1``.
+ - If ``self`` is ``False``, the result is ``0``.
Parameters
----------
self: array
- zero-dimensional array instance. Must have a real-valued floating-point data type.
+ zero-dimensional array instance. Should have a real-valued or boolean data type. If ``self`` has a complex floating-point data type, the function must raise a ``TypeError``.
Returns
-------
@@ -483,7 +532,7 @@ def __index__(self: array, /) -> int:
Parameters
----------
self: array
- zero-dimensional array instance. Must have an integer data type.
+ zero-dimensional array instance. Should have an integer data type. If ``self`` has a floating-point data type, the function must raise a ``TypeError``.
Returns
-------
@@ -493,17 +542,37 @@ def __index__(self: array, /) -> int:
def __int__(self: array, /) -> int:
"""
- Converts a zero-dimensional integer array to a Python ``int`` object.
+ Converts a zero-dimensional array to a Python ``int`` object.
+
+ **Special cases**
+
+ For boolean operands,
+
+ - If ``self`` is ``True``, the result is ``1``.
+ - If ``self`` is ``False``, the result is ``0``.
+
+ For floating-point operands,
+
+ - If ``self`` is a finite number, the result is the integer part of ``self``.
+ - If ``self`` is ``-0``, the result is ``0``.
Parameters
----------
self: array
- zero-dimensional array instance. Must have an integer data type.
+ zero-dimensional array instance. Should have a real-valued or boolean data type. If ``self`` has a complex floating-point data type, the function must raise a ``TypeError``.
Returns
-------
out: int
a Python ``int`` object representing the single element of the array instance.
+
+
+ **Raises**
+
+ For floating-point operands,
+
+ - If ``self`` is either ``+infinity`` or ``-infinity``, raise ``OverflowError``.
+ - If ``self`` is ``NaN``, raise ``ValueError``.
"""
def __invert__(self: array, /) -> array:
diff --git a/spec/API_specification/array_object.rst b/spec/API_specification/array_object.rst
index 758e08582..b45e41987 100644
--- a/spec/API_specification/array_object.rst
+++ b/spec/API_specification/array_object.rst
@@ -283,6 +283,7 @@ Methods
array.__and__
array.__array_namespace__
array.__bool__
+ array.__complex__
array.__dlpack__
array.__dlpack_device__
array.__eq__
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