Add AbstractRealQuantity

[MilesCranmer]

This adds a new AbstractRealQuantity <: Real and a concrete type RealQuantity. Users can wrap quantities with RealQuantity(0.3u"km/s") to pass to functions that require real input. But the default would still be Quantity <: Number for reasons discussed here.

I also introduce a new function promote_quantity which one can overload as a sort of custom type hierarchy, so that RealQuantity -> Quantity if it interacts with a non-real, and {RealQuantity,Quantity} -> GenericQuantity if they interact with non-numeric.

However this is a bit of a mess right now due to promotion complexities, making (0.3+2im)u"km/s" promote to a Complex{<:Quantity} instead of a Quantity... Anybody interested in having a go? Fixed!

[github-actions[bot]]

Benchmark Results

	main	0609463b8f1863...	t[main]/t[0609463b8f1863...]
Quantity/creation/Quantity(x)	3.1 ± 0.01 ns	2.79 ± 0.01 ns	1.11
Quantity/creation/Quantity(x, length=y)	3.11 ± 0.01 ns	3.11 ± 0.01 ns	1
Quantity/with_numbers/*real	3.1 ± 0.01 ns	3.1 ± 0.01 ns	1
Quantity/with_numbers/^int	8.37 ± 2.5 ns	8.05 ± 2.2 ns	1.04
Quantity/with_numbers/^int * real	8.37 ± 2.5 ns	8.05 ± 2.2 ns	1.04
Quantity/with_quantity/+y	5.27 ± 0.01 ns	5.27 ± 0.01 ns	1
Quantity/with_quantity//y	3.11 ± 0.001 ns	3.41 ± 0.01 ns	0.912
Quantity/with_self/dimension	1.55 ± 0.01 ns	1.55 ± 0.01 ns	1
Quantity/with_self/inv	3.11 ± 0.001 ns	3.11 ± 0.01 ns	1
Quantity/with_self/ustrip	1.55 ± 0.01 ns	1.56 ± 0.01 ns	0.994
QuantityArray/broadcasting/multi_array_of_quantities	0.147 ± 0.016 ms	0.15 ± 0.14 ms	0.985
QuantityArray/broadcasting/multi_normal_array	0.0499 ± 0.003 ms	0.053 ± 0.00026 ms	0.941
QuantityArray/broadcasting/multi_quantity_array	0.158 ± 0.00092 ms	0.158 ± 0.00072 ms	0.999
QuantityArray/broadcasting/x^2_array_of_quantities	26.5 ± 3.3 μs	27.2 ± 1.9 μs	0.976
QuantityArray/broadcasting/x^2_normal_array	4.35 ± 0.85 μs	5.19 ± 0.83 μs	0.838
QuantityArray/broadcasting/x^2_quantity_array	6.97 ± 0.27 μs	6.03 ± 0.4 μs	1.16
QuantityArray/broadcasting/x^4_array_of_quantities	0.0788 ± 0.00078 ms	0.0787 ± 0.00055 ms	1
QuantityArray/broadcasting/x^4_normal_array	0.0498 ± 0.00015 ms	0.0498 ± 0.00018 ms	0.998
QuantityArray/broadcasting/x^4_quantity_array	0.0592 ± 0.00016 ms	0.0593 ± 0.00019 ms	0.998
time_to_load	0.162 ± 0.006 s	0.238 ± 0.0058 s	0.681

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]

Actually I think we shouldn't make all default quantities Real. We can just have these as quantities that someone can use if they want that particular dispatch.

[MilesCranmer]

@gaurav-arya I'm wondering if we should just make Quantity <: Real, and NumberQuantity <: Number. Having the default numeric type be RealQuantity rather than Quantity could be a bit awkward...

[gaurav-arya]

Actually I think we shouldn't make all default quantities Real. We can just have these as quantities that someone can use if they want that particular dispatch.

Why not choose the most specific type given the value type? E.g. 1.0 * u"m" would be <: Real but (1.0 + 1.0 * im) * u"m" would be <: Number for now, etc. Is there a disadvantage, i.e. a reason the user would have preferred Quantity{<:Real} as opposed to RealQuantity{<:Real}?

In this scenario, I wonder if we even need a single DEFAULT_QUANTITY_TYPE? Instead, we have a default mapping from value type -> quantity type?

[MilesCranmer]

Why not choose the most specific type given the value type? E.g. 1.0 * u"m" would be <: Real but (1.0 + 1.0 * im) * u"m" would be <: Number for now, etc. Is there a disadvantage, i.e. a reason the user would have preferred Quantity{<:Real} as opposed to RealQuantity{<:Real}?

Yeah good point. The current behavior in this PR is actually (1.0 * u"m")::Real and ((1.0 + 1.0 * im) * u"m")::Number already. But I'm wondering if we should change this...

In this scenario, I wonder if we even need a single DEFAULT_QUANTITY_TYPE? Instead, we have a default mapping from value type -> quantity type?

Maybe do you mean like #66? Although I don't think we necessarily need an AbstractFloatQuantity yet, unless a specific need arises, since it will increase load time. But AbstractRealQuantity seems necessary for many packages.

[MilesCranmer]

Cool, coverage is now back to 100%. Feel free to take a look when you want. I'll keep RealQuantity as the default, but am still open to changing the name to be Quantity and NumberQuantity rather than RealQuantity and Quantity, respectively.

[MilesCranmer]

Also:

Why not choose the most specific type given the value type? E.g. 1.0 * u"m" would be <: Real

Is this semantically correct? One could indeed argue that 1.0 meters is a type of number... But is it a real?

Let me give an example. Would you agree with the statement

$(0.5 \text{ km} \text{ s}^{-1}) \in \mathbb{R}$

? I think it kind of seems incorrect... It's more like:

$(0.5 \text{ km} \text{ s}^{-1}) \in \mathbb{R} \times \mathbb{U}$

for some abstract space $\mathbb{U}$ of physical dimensions. In which case it might not be the best option to set the default type as ::Real.

Whereas Number is much more abstract and I could totally say that a physical quantity is a type of number. i.e., $\mathbb{R} \times \mathbb{U}$ is a space of "numbers."

This semantic ambiguity leads me to want to keep Quantity <: Number as the default, but allow RealQuantity as a wrapper for users who know what they are doing. Wdyt?

[MilesCranmer]

Thanks!