8000 Add complex number support to `exp` by kgryte · Pull Request #451 · data-apis/array-api · GitHub
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Add complex number support to exp #451

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Merged
merged 8 commits into from
Jul 7, 2022
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Add complex number support to exp #451

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b23b0fc
Update ignore file
kgryte Jun 13, 2022
ba07d69
Add complex number support to `exp`
kgryte Jun 13, 2022
bffddb2
Update input and output data types
kgryte Jun 13, 2022
d10b63b
Update description to accommodate complex number input
kgryte Jun 13, 2022
f84e176
Add note concerning complex conjugation
kgryte Jun 13, 2022
cb2c8df
Specify special case in terms of `cis` function
kgryte Jun 13, 2022
2b5028c
Fix special cases and move note
kgryte Jun 20, 2022
9908911
Fix `cis` argument
kgryte Jun 20, 2022
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Specify special case in terms of cis function
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@kgryte
kgryte committed Jun 13, 2022
commit cb2c8df2e76c61be36099c6060dfc7dbab6302c3
6 changes: 4 additions & 2 deletions spec/API_specification/array_api/elementwise_functions.py
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Expand Up @@ -537,8 +537,8 @@ def exp(x: array, /) -> array:
- 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 either ``+0`` or ``-0``, the result is ``infinity + 0j``.
- If ``a`` is ``-infinity`` and ``b`` is a finite number, the result is ``0 + 0j``.
- If ``a`` is ``+infinity`` and ``b`` is a nonzero finite number, the result is ``infinity + infinity j``.
- If ``a`` is ``-infinity`` and ``b`` is a finite number, the result is ``+0 * cis(x_i)``.
- If ``a`` is ``+infinity`` and ``b`` is a nonzero finite number, the result is ``+infinity * cis(x_i)``.
- 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).
Expand All @@ -547,6 +547,8 @@ def exp(x: array, /) -> array:
- 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(x_i)`` is ``cos(x_i) + sin(x_i)*1j``.

.. note::
The exponential function is an entire function in the complex plane and has no branch cuts.

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