diff --git a/.gitignore b/.gitignore
index 73e203a64..86bab2717 100644
--- a/.gitignore
+++ b/.gitignore
@@ -30,3 +30,4 @@ node_modules/
__pycache__/
*.pyc
spec/**/generated
+tmp/
\ No newline at end of file
diff --git a/spec/API_specification/array_api/elementwise_functions.py b/spec/API_specification/array_api/elementwise_functions.py
index 7acefaf52..d5a560417 100644
--- a/spec/API_specification/array_api/elementwise_functions.py
+++ b/spec/API_specification/array_api/elementwise_functions.py
@@ -223,8 +223,8 @@ def atan2(x1: array, x2: array, /) -> array:
- If ``x1_i`` is greater than ``0``, ``x1_i`` is a finite number, and ``x2_i`` is ``-infinity``, the result is an implementation-dependent approximation to ``+π``.
- If ``x1_i`` is less than ``0``, ``x1_i`` is a finite number, and ``x2_i`` is ``+infinity``, the result is ``-0``.
- If ``x1_i`` is less than ``0``, ``x1_i`` is a finite number, and ``x2_i`` is ``-infinity``, the result is an implementation-dependent approximation to ``-π``.
- - If ``x1_i`` is ``+infinity`` and ``x2_i`` is finite, the result is an implementation-dependent approximation to ``+π/2``.
- - If ``x1_i`` is ``-infinity`` and ``x2_i`` is finite, the result is an implementation-dependent approximation to ``-π/2``.
+ - If ``x1_i`` is ``+infinity`` and ``x2_i`` is a finite number, the result is an implementation-dependent approximation to ``+π/2``.
+ - If ``x1_i`` is ``-infinity`` and ``x2_i`` is a finite number, the result is an implementation-dependent approximation to ``-π/2``.
- If ``x1_i`` is ``+infinity`` and ``x2_i`` is ``+infinity``, the result is an implementation-dependent approximation to ``+π/4``.
- If ``x1_i`` is ``+infinity`` and ``x2_i`` is ``-infinity``, the result is an implementation-dependent approximation to ``+3π/4``.
- If ``x1_i`` is ``-infinity`` and ``x2_i`` is ``+infinity``, the result is an implementation-dependent approximation to ``-π/4``.
@@ -519,11 +519,11 @@ def equal(x1: array, x2: array, /) -> array:
def exp(x: array, /) -> array:
"""
- Calculates an implementation-dependent approximation to the exponential function, having domain ``[-infinity, +infinity]`` and codomain ``[+0, +infinity]``, for each element ``x_i`` of the input array ``x`` (``e`` raised to the power of ``x_i``, where ``e`` is the base of the natural logarithm).
+ Calculates an implementation-dependent approximation to the exponential function for each element ``x_i`` of the input array ``x`` (``e`` raised to the power of ``x_i``, where ``e`` is the base of the natural logarithm).
**Special cases**
- For floating-point operands,
+ For real-valued floating-point operands,
- If ``x_i`` is ``NaN``, the result is ``NaN``.
- If ``x_i`` is ``+0``, the result is ``1``.
@@ -531,15 +531,39 @@ def exp(x: array, /) -> array:
- If ``x_i`` is ``+infinity``, the result is ``+infinity``.
- If ``x_i`` is ``-infinity``, the result is ``+0``.
+ For complex floating-point operands, let ``a = real(x_i)``, ``b = imag(x_i)``, and
+
+ .. note::
+ For complex floating-point operands, ``exp(conj(x))`` must equal ``conj(exp(x))``.
+
+ - If ``a`` is either ``+0`` or ``-0`` and ``b`` is ``+0``, the result is ``1 + 0j``.
+ - If ``a`` is a finite number and ``b`` is ``+infinity``, the result is ``NaN + NaN j``.
+ - If ``a`` is a finite number and ``b`` is ``NaN``, the result is ``NaN + NaN j``.
+ - If ``a`` is ``+infinity`` and ``b`` is ``+0``, the result is ``infinity + 0j``.
+ - If ``a`` is ``-infinity`` and ``b`` is a finite number, the result is ``+0 * cis(b)``.
+ - If ``a`` is ``+infinity`` and ``b`` is a nonzero finite number, the result is ``+infinity * cis(b)``.
+ - If ``a`` is ``-infinity`` and ``b`` is ``+infinity``, the result is ``0 + 0j`` (signs of real and imaginary components are unspecified).
+ - If ``a`` is ``+infinity`` and ``b`` is ``+infinity``, the result is ``infinity + NaN j`` (sign of real component is unspecified).
+ - If ``a`` is ``-infinity`` and ``b`` is ``NaN``, the result is ``0 + 0j`` (signs of real and imaginary components are unspecified).
+ - If ``a`` is ``+infinity`` and ``b`` is ``NaN``, the result is ``infinity + NaN j`` (sign of real component is unspecified).
+ - If ``a`` is ``NaN`` and ``b`` is ``+0``, the result is ``NaN + 0j``.
+ - If ``a`` is ``NaN`` and ``b`` is not equal to ``0``, the result is ``NaN + NaN j``.
+ - If ``a`` is ``NaN`` and ``b`` is ``NaN``, the result is ``NaN + NaN j``.
+
+ where ``cis(v)`` is ``cos(v) + sin(v)*1j``.
+
+ .. note::
+ The exponential function is an entire function in the complex plane and has no branch cuts.
+
Parameters
----------
x: array
- input array. Should have a real-valued floating-point data type.
+ input array. Should have a floating-point data type.
Returns
-------
out: array
- an array containing the evaluated exponential function result for each element in ``x``. The returned array must have a real-valued floating-point data type determined by :ref:`type-promotion`.
+ an array containing the evaluated exponential function result for each element in ``x``. The returned array must have a floating-point data type determined by :ref:`type-promotion`.
"""
def expm1(x: array, /) -> array:
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