Simple affine units implementation

[MilesCranmer]

@Deduction42

Here is a reduced version of #159 with only the basic functionality. Writing out degC will auto-convert to dimensions when you multiply it with a number:

julia> x = 22ua"degC"
295.15 K

julia> x = 0ua"degC"
273.15 K

julia> 50ua"degC" - 40ua"degF"
45.55555555555554 K

That's basically it. I think this gets the main feature of unit parsing but without needing to have a separate AffineDimensions object that requires a lot of patching throughout the library.

[github-actions]

Benchmark Results

	main	9c0f1ab...	main / 9c0f1ab...
Quantity/creation/Quantity(x)	3.1 ± 0.01 ns	3.1 ± 0.01 ns	0.997
Quantity/creation/Quantity(x, length=y)	3.43 ± 0.011 ns	3.73 ± 0.01 ns	0.919
Quantity/with_numbers/*real	3.11 ± 0.001 ns	3.11 ± 0.001 ns	1
Quantity/with_numbers/^int	8.68 ± 1.6 ns	8.68 ± 1.6 ns	1
Quantity/with_numbers/^int * real	8.98 ± 1.6 ns	8.99 ± 1.6 ns	0.999
Quantity/with_quantity/+y	4.35 ± 0.001 ns	4.35 ± 0.01 ns	1
Quantity/with_quantity//y	3.11 ± 0.001 ns	3.42 ± 0.001 ns	0.909
Quantity/with_self/dimension	3.11 ± 0.91 ns	2.79 ± 0.001 ns	1.11
Quantity/with_self/inv	3.11 ± 0.001 ns	3.11 ± 0 ns	1
Quantity/with_self/ustrip	3.72 ± 0.011 ns	2.79 ± 0 ns	1.33
QuantityArray/broadcasting/multi_array_of_quantities	0.0873 ± 0.0012 ms	0.0877 ± 0.0017 ms	0.996
QuantityArray/broadcasting/multi_normal_array	0.0528 ± 0.0003 ms	0.0496 ± 0.0019 ms	1.06
QuantityArray/broadcasting/multi_quantity_array	0.0592 ± 0.0061 ms	0.0559 ± 0.0031 ms	1.06
QuantityArray/broadcasting/x^2_array_of_quantities	13.7 ± 1.5 μs	14.9 ± 2.5 μs	0.921
QuantityArray/broadcasting/x^2_normal_array	2.1 ± 0.63 μs	2.35 ± 1.4 μs	0.894
QuantityArray/broadcasting/x^2_quantity_array	6.5 ± 0.31 μs	6.48 ± 0.23 μs	1
QuantityArray/broadcasting/x^4_array_of_quantities	0.0811 ± 0.00089 ms	0.0815 ± 0.0012 ms	0.995
QuantityArray/broadcasting/x^4_normal_array	0.0496 ± 0.0032 ms	0.0466 ± 0.0024 ms	1.07
QuantityArray/broadcasting/x^4_quantity_array	0.059 ± 0.0063 ms	0.0498 ± 0.0092 ms	1.19
time_to_load	0.201 ± 0.0062 s	0.202 ± 0.0042 s	0.995

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR.
Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

[Deduction42]

What kind of object does ua"degC" return? Does ua"m/s" work too?

[MilesCranmer]

ua"degC" returns an AffineUnits object. It's outside of the dimensions hierarchy and thus can't be used inside a Quantity. Only when you multiply this against a number does it become a quantity.

ua"m/s" at the moment does in fact work; it triggers a fall-back method that calls uparse.

(Though I was thinking of deleting that, so users would need to be very explicit about getting an AffineUnits object)

[Deduction42]

I'd actually prefer a string macro that produced units, so this looks like a very clever fix. As long 'ua"..."' and 'aff_uparse("...")' produces a consistent object (AffineUnits) and works on any units in the registry, this is probably good enough for most basic use cases. Are you able to convert a quantity back to affine units? I typically only use this worklow:

{customer units}->{si units}->{numbers}->{algorithm}->{si units}->{customer units}

[MilesCranmer]

There’s no conversion to affine units, only from affine to SI. Right now there’s not even a display in affine units, because you would never use a naked AffineUnits for anything. (Edit: I added a display for the naked units, just because it was a one-line change, I think it's ok)

I feel the reverse from SI to affine + printing might be ok to do in user code, so I don't see a huge need to add it here.

Also, why do you need the other units accessible in ua_str? Since they are incompatible with affine anyways. Why not just do a

try
    uparse(s)
catch
    aff_uparse(s)
end

I don’t know why DQ would need to do this internally.

[MilesCranmer]

Ok I am pretty happy with this. From 744 to 217 lines compared to #159, and gets the main functionality without the difficulties of treating affine units as regular Quantity. Will merge soon.

Note that I am labelling everything as "experimental" so there's the opportunity to roll things back or make changes if needed.