Parsing of logarithmic units

Start at the cf_xarray.units units entry point and reproduce the reported units("lg(re mg.m-3)") failure. Check how the Pint registry handles this expression and identify the relevant existing tests, if any. Done means the documented logarithmic unit no longer raises UndefinedUnitError and the behavior is covered by a regression test.

Hi,
I'm working with data files having units provided as lg(re mg.m-3), which according to the udunits documentation here is valid.
However trying to parse this with the units module of cf_xarrays seems to crash:

In [5]: from cf_xarray.units import units

In [6]: units("lg(re mg.m-3)")
---------------------------------------------------------------------------
UndefinedUnitError                        Traceback (most recent call last)
Cell In[6], line 1
----> 1 units("lg(re mg.m-3)")

File ~/mambaforge/envs/satpy/lib/python3.11/site-packages/pint/facets/plain/registry.py:1264, in PlainRegistry.parse_expression(self, input_string, case_sensitive, use_decimal, **values)
   1261 input_string = string_preprocessor(input_string)
   1262 gen = tokenizer(input_string)
-> 1264 return build_eval_tree(gen).evaluate(
   1265     lambda x: self._eval_token(x, case_sensitive=case_sensitive, **values)
   1266 )

File ~/mambaforge/envs/satpy/lib/python3.11/site-packages/pint/pint_eval.py:114, in EvalTreeNode.evaluate(self, define_op, bin_op, un_op)
    112     if op_text not in bin_op:
    113         raise DefinitionSyntaxError('missing binary operator "%s"' % op_text)
--> 114     left = self.left.evaluate(define_op, bin_op, un_op)
    115     return bin_op[op_text](left, self.right.evaluate(define_op, bin_op, un_op))
    116 elif self.operator:
    117     # unary operator

File ~/mambaforge/envs/satpy/lib/python3.11/site-packages/pint/pint_eval.py:124, in EvalTreeNode.evaluate(self, define_op, bin_op, un_op)
    121     return un_op[op_text](self.left.evaluate(define_op, bin_op, un_op))
    122 else:
    123     # single value
--> 124     return define_op(self.left)

File ~/mambaforge/envs/satpy/lib/python3.11/site-packages/pint/facets/plain/registry.py:1265, in PlainRegistry.parse_expression.<locals>.<lambda>(x)
   1261 input_string = string_preprocessor(input_string)
   1262 gen = tokenizer(input_string)
   1264 return build_eval_tree(gen).evaluate(
-> 1265     lambda x: self._eval_token(x, case_sensitive=case_sensitive, **values)
   1266 )

File ~/mambaforge/envs/satpy/lib/python3.11/site-packages/pint/facets/plain/registry.py:1151, in PlainRegistry._eval_token(self, token, case_sensitive, use_decimal, **values)
   1146         return self.Quantity(values[token_text])
   1147     else:
   1148         return self.Quantity(
   1149             1,
   1150             self.UnitsContainer(
-> 1151                 {self.get_name(token_text, case_sensitive=case_sensitive): 1}
   1152             ),
   1153         )
   1154 elif token_type == NUMBER:
   1155     return ParserHelper.eval_token(token, non_int_type=self.non_int_type)

File ~/mambaforge/envs/satpy/lib/python3.11/site-packages/pint/facets/plain/registry.py:599, in PlainRegistry.get_name(self, name_or_alias, case_sensitive)
    597 candidates = self.parse_unit_name(name_or_alias, case_sensitive)
    598 if not candidates:
--> 599     raise UndefinedUnitError(name_or_alias)
    600 elif len(candidates) == 1:
    601     prefix, unit_name, _ = candidates[0]

UndefinedUnitError: 'lg' is not defined in the unit registry

I guess this is not implemented. Anything I can do to help with this?