Refactor symbolic units module, make all symbols available at import

[MilesCranmer]

Previously, units were created the first time the user used sym_uparse, because otherwise it required creating ~150 arrays at import inside an @eval. This also means that you could not precompile unit calculations done with symbolic units.

With this change, we now eagerly create symbolic units as immutable objects. For example, h would be created with

Quantity(1.0, SymbolicDimensionsSingleton(:h))

and this would represented in memory as the lightweight (1.0, 85), where 85 is the index of hours in the constant tuple of units and quantities.

• This creates the abstract type AbstractSymbolicDimensions <: AbstractDimensions and defines several of the symbolic dimensions methods on it.
• This uses a new type SymbolicDimensionsSingleton that stores a single integer corresponding to the index of the unit/constant in a constant tuple.
• This also exports modules SymbolicUnits and SymbolicConstants, so you can do things like:

julia> using DynamicQuantities

julia> using DynamicQuantities.SymbolicUnits: km, h

julia> km |> typeof
Quantity{Float64, SymbolicDimensionsSingleton{DynamicQuantities.FixedRational{Int32, 25200}}}

julia> km/h |> typeof
Quantity{Float64, SymbolicDimensions{DynamicQuantities.FixedRational{Int32, 25200}}}

julia> km/h |> uexpand
0.2777777777777778 m s⁻¹

julia> km/h |> uexpand |> uconvert(SymbolicConstants.pc / SymbolicUnits.Myr)
0.00028408671251269307 Myr⁻¹ pc

@devmotion would you be up for reviewing this?

---

cc @gaurav-arya

Fixes #51 by cadojo (and prevents the need for #58)

[github-actions[bot]]

Benchmark Results

	main	212626fdd9c169...	t[main]/t[212626fdd9c169...]
Quantity/creation/Quantity(x)	2.79 ± 0.009 ns	3.41 ± 0.01 ns	0.82
Quantity/creation/Quantity(x, length=y)	3.41 ± 0.01 ns	3.11 ± 0.01 ns	1.1
Quantity/with_numbers/*real	3.1 ± 0.01 ns	3.1 ± 0.01 ns	1
Quantity/with_numbers/^int	8.05 ± 1.9 ns	8.05 ± 2.2 ns	1
Quantity/with_numbers/^int * real	8.36 ± 1.9 ns	8.67 ± 2.2 ns	0.964
Quantity/with_quantity/+y	4.04 ± 0.001 ns	4.04 ± 0.001 ns	1
Quantity/with_quantity//y	3.11 ± 0.001 ns	3.42 ± 0.01 ns	0.909
Quantity/with_self/dimension	3.1 ± 0.01 ns	3.1 ± 0.01 ns	1
Quantity/with_self/inv	3.11 ± 0.01 ns	3.11 ± 0.001 ns	1
Quantity/with_self/ustrip	2.79 ± 0.009 ns	2.79 ± 0.01 ns	1
QuantityArray/broadcasting/multi_array_of_quantities	0.149 ± 0.0016 ms	0.145 ± 0.00089 ms	1.03
QuantityArray/broadcasting/multi_normal_array	0.0529 ± 0.00015 ms	0.0528 ± 0.00017 ms	1
QuantityArray/broadcasting/multi_quantity_array	0.158 ± 0.00054 ms	0.155 ± 0.00078 ms	1.02
QuantityArray/broadcasting/x^2_array_of_quantities	22.9 ± 1.5 μs	23.1 ± 1.4 μs	0.992
QuantityArray/broadcasting/x^2_normal_array	4.37 ± 1.3 μs	4.06 ± 1.3 μs	1.08
QuantityArray/broadcasting/x^2_quantity_array	6.95 ± 0.25 μs	6.92 ± 0.24 μs	1
QuantityArray/broadcasting/x^4_array_of_quantities	0.0786 ± 0.00047 ms	0.0785 ± 0.00038 ms	1
QuantityArray/broadcasting/x^4_normal_array	0.0498 ± 0.00016 ms	0.0467 ± 0.00017 ms	1.07
QuantityArray/broadcasting/x^4_quantity_array	0.0499 ± 0.00015 ms	0.0501 ± 0.0031 ms	0.995
time_to_load	0.124 ± 0.00053 s	0.129 ± 0.0036 s	0.956

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).

[MilesCranmer]

@gaurav-arya I wonder if there are any type instabilities that could potentially come from this...? Although the promotion rules seem to be doing their job:

julia> [km]
1-element Vector{Quantity{Float64, SymbolicDimensionsSingleton{DynamicQuantities.FixedRational{Int32, 25200}}}}:
 1.0 km

julia> [km, km/h]
2-element Vector{Quantity{Float64, SymbolicDimensions{DynamicQuantities.FixedRational{Int32, 25200}}}}:
     1.0 km
 1.0 km h⁻¹

julia> [km, km/h, uexpand(km)]
3-element Vector{Quantity{Float64, Dimensions{DynamicQuantities.FixedRational{Int32, 25200}}}}:
                 1000.0 m
 0.2777777777777778 m s⁻¹
                 1000.0 m

I guess you could create an instability if you do something like output=km; output /= h, but in that case you would be asking for type instabilities anyways...

[gaurav-arya]

It'll take me a bit of time since I'm not quite done with school yet, but I'll give this a review:)

[MilesCranmer]

Thanks very much for the suggestions @devmotion. Everything implemented!

[MilesCranmer]

Let me know if there are any other comments! Otherwise I will try to merge this soon.