cmath.log has an invalid signature

[mdickinson]

BPO	45218
Nosy	@mdickinson, @vstinner, @corona10

^{Note: these values reflect the state of the issue at the time it was migrated and might not reflect the current state.}

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GitHub fields:

assignee = None
closed_at = None
created_at = <Date 2021-09-16.09:09:00.708>
labels = ['extension-modules', 'type-bug', '3.9', '3.10', '3.11']
title = 'cmath.log has an invalid signature'
updated_at = <Date 2021-09-24.15:55:05.789>
user = 'https://github.com/mdickinson'

bugs.python.org fields:

activity = <Date 2021-09-24.15:55:05.789>
actor = 'corona10'
assignee = 'none'
closed = False
closed_date = None
closer = None
components = ['Extension Modules']
creation = <Date 2021-09-16.09:09:00.708>
creator = 'mark.dickinson'
dependencies = []
files = []
hgrepos = []
issue_num = 45218
keywords = []
message_count = 5.0
messages = ['401933', '401937', '401938', '401939', '401940']
nosy_count = 3.0
nosy_names = ['mark.dickinson', 'vstinner', 'corona10']
pr_nums = []
priority = 'normal'
resolution = None
stage = None
status = 'open'
superseder = None
type = 'behavior'
url = 'https://bugs.python.org/issue45218'
versions = ['Python 3.9', 'Python 3.10', 'Python 3.11']

Linked PRs

• gh-89381: Fix invalid signatures of math/cmath.log #101070
• gh-89381: Fix signature for math.log and cmath.log #101115
• gh-89381: Fix invalid signatures of math/cmath.log #101404
• Revert "gh-89381: Fix invalid signatures of math/cmath.log (#101404)" #101580
• gh-89381: Fix invalid signatures of math/cmath.log (v2) #101593

[mdickinson]

inspect.signature reports that the cmath.log function has an invalid signature:

Python 3.11.0a0 (heads/fix-44954:d0ea569eb5, Aug 19 2021, 14:59:04) [Clang 12.0.0 (clang-1200.0.32.29)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> import cmath
>>> import inspect
>>> inspect.signature(cmath.log)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/Users/mdickinson/Python/cpython/Lib/inspect.py", line 3215, in signature
    return Signature.from_callable(obj, follow_wrapped=follow_wrapped,
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/mdickinson/Python/cpython/Lib/inspect.py", line 2963, in from_callable
    return _signature_from_callable(obj, sigcls=cls,
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/mdickinson/Python/cpython/Lib/inspect.py", line 2432, in _signature_from_callable
    return _signature_from_builtin(sigcls, obj,
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/mdickinson/Python/cpython/Lib/inspect.py", line 2244, in _signature_from_builtin
    return _signature_fromstr(cls, func, s, skip_bound_arg)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/Users/mdickinson/Python/cpython/Lib/inspect.py", line 2114, in _signature_fromstr
    raise ValueError("{!r} builtin has invalid signature".format(obj))
    ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
ValueError: <built-in function log> builtin has invalid signature

[mdickinson]

Issue bpo-43067 is similar. I'm not sure what the best solution is in this case:

• un-argument-clinic cmath.log, and document the signature using two lines (similar to range):

     log(z)
     log(z, base)

• change the behaviour of cmath.log so that the second argument is allowed be None (and defaults to None)

[mdickinson]

See also bpo-36306 and bpo-29299. There may be nothing to be done here, but it would be nice if math.log and cmath.log at least behaved in the same way. A default of None doesn't seem like a terrible option.

(BTW, just to forestall the suggestion, a default of math.e or cmath.e is definitely not the right thing to use as a default: math.e is not exactly Euler's value for e, and log base math.e is likely to be less accurate than plain natural log.)

[mdickinson]

and log base math.e is likely to be less accurate than plain natural log

Nope, that's nonsense, since the two-argument form simply divides by log(base), and while log(math.e) is mathematically not exactly 1 (its exact value, assuming IEEE 754 binary64, starts 0.9999999999999999468176229339410862948..., which is off from 1.0 by around 0.48 ulps), it's *just* close enough that with a well-behaved libm log implementation it's exactly 1.0 after rounding.

I still don't like the idea of math.e as a default value here, but I'd have to work harder to identify why it makes me uneasy.

[vstinner]

The current Argument Clinic syntax for math.log() is:

--------------
/*[clinic input]
math.log

x:    object
[
base: object(c_default="NULL") = math.e
]
/

Return the logarithm of x to the given base.
(...)
--------------

math.log.__text_signature__ is None. __text_signature__ is used by inspect.signature().

I guess that it's a bug in Argument Clinic.