Possibility of support for CF/UDUNITS-style powers of units

[jthielen]

The CF Conventions are a common standard used in the atmospheric and oceanic sciences, and many NetCDF files follow these conventions. The unit conventions rely upon the UDUNITS package. While most CF/UDUNITS-compliant unit strings can be parsed properly by pint, I've run into some issues recently with powers of units in the default symbol notation, i.e., strings such as "m2 s-2" for meters squared per second squared.

Would support for powers of units in this style be welcome in pint?

If so, this should be fairly simple to implement by adding the following regex substitution pair

(r'(?<=[A-Za-z])(?![A-Za-z])(?<![0-9\-])(?=[0-9\-])', '**')

to

pint/pint/util.py

Lines 565 to 575 in 2afdc4b

	#: List of regex substitution pairs.
	_subs_re = [('\N{DEGREE SIGN}', " degree"),
	(r"([\w\.\-\+\*\\\^])\s+", r"\1 "), # merge multiple spaces
	(r"({}) squared", r"\1**2"), # Handle square and cube
	(r"({}) cubed", r"\1**3"),
	(r"cubic ({})", r"\1**3"),
	(r"square ({})", r"\1**2"),
	(r"sq ({})", r"\1**2"),
	(r"\b([0-9]+\.?[0-9]*)(?=[e|E][a-zA-Z]|[a-df-zA-DF-Z])", r"\1*"), # Handle numberLetter for multiplication
	(r"([\w\.\-])\s+(?=\w)", r"\1*"), # Handle space for multiplication
	]

If not, would it be possible to add something to the registry API in order to add regex substitution pairs for the string preprocessor? Even if pint itself doesn't wish to support this style of powers of units (which would be reasonable...this isn't the clearest syntax), having some officially supported way to add new regex substitutions would make it much easier for downstream libraries like MetPy to implement it if desired for CF/UDUNITS-compatibility.

Either way, I'd be glad to put in a PR to implement the desired functionality.

xref Unidata/MetPy#1134

[hgrecco]

I would answer in different converging directions:

1. There has been an idea to create an API to edit replacements. See a very early discussion parse_expression fails on units with spaces in the name #799
2. I would agree to add any default replacement that does not create ambiguity. For example s-2 could mean s minus 2.
3. (item 2) could be relaxed if we clearly separate in the docs parse_units from parse_expression

[jthielen]

Thank you for bringing up the point about ambiguity, and after thinking about it more, I'm not sure if there is a way to avoid it given pint's existing behavior and UDUNITS behavior.

While this is a contrived example, I think it demonstrates the ambiguity well:

In pint:

import pint
ureg = pint.UnitRegistry()
test_str = '1e6 Hz s-2'
print(ureg(test_str))

999998.0 dimensionless

In cf_units (a python wrapper for UDUNITS):

from cf_units import Unit
test_str = '1e6 Hz s-2'
print(Unit(test_str).definition)

1000000 s-3

Also, because of the expressions that CF/UDUNITS allows, it would likely require using parse_expression, so I'm not sure if relaxing the unambiguity requirement by clearly separating parse_units and parse_expression would be sufficient (unless I'm misinterpreting something).

With all that in mind, I think the best way forward will be building on the early discussions for an API to extend replacements and/or the pre-processor itself (#429 (comment))? I will try putting together an initial PR sometime soon.