diff --git a/spec/API_specification/array_api/elementwise_functions.py b/spec/API_specification/array_api/elementwise_functions.py
index e76be8d65..34484162d 100644
--- a/spec/API_specification/array_api/elementwise_functions.py
+++ b/spec/API_specification/array_api/elementwise_functions.py
@@ -1351,19 +1351,38 @@ def round(x: array, /) -> array:
"""
def sign(x: array, /) -> array:
- """
+ r"""
Returns an indication of the sign of a number for each element ``x_i`` of the input array ``x``.
+ The sign function (also known as the **signum function**) of a number :math:`x_i` is defined as
+
+ .. math::
+ \operatorname{sign}(x_i) = \begin{cases}
+ 0 & \textrm{if } x_i = 0 \\
+ \frac{x}{|x|} & \textrm{otherwise}
+ \end{cases}
+
+ where :math:`|x_i|` is the absolute value of :math:`x_i`.
+
**Special cases**
+ For real-valued operands,
+
- If ``x_i`` is less than ``0``, the result is ``-1``.
- If ``x_i`` is either ``-0`` or ``+0``, the result is ``0``.
- If ``x_i`` is greater than ``0``, the result is ``+1``.
+ - If ``x_i`` is ``NaN``, the result is ``NaN``.
+
+ For complex floating-point operands, let ``a = real(x_i)``, ``b = imag(x_i)``, and
+
+ - If ``a`` is either ``-0`` or ``+0`` and ``b`` is either ``-0`` or ``+0``, the result is ``0 + 0j``.
+ - If ``a`` is ``NaN`` or ``b`` is ``NaN``, the result is ``NaN + NaN j``.
+ - In the remaining cases, special cases must be handled according to the rules of complex number division (see :func:`~array_api.divide`).
Parameters
----------
x: array
- input array. Should have a real-valued data type.
+ input array. Should have a numeric data type.
Returns
-------
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