Equality between `Gain`s is not transitive, prevents correct hashing

[sostock]

When comparing a power gain Gain{L, :p} and a root-power gain Gain{L, :rp} with the same L, they get promoted to Gain{L, :?} without changing their numerical values. This breaks the transitivity of ==:

julia> a = Gain{Unitful.Decibel, :rp}(20) # 20 dB (root-power) == factor 10
20 dB

julia> b = Gain{Unitful.Decibel, :p}(20) # 20 dB (power) == factor 100
20 dB

julia> c = Gain{Unitful.Bel, :p}(2) # 2 B (power) == factor 100
2 B

julia> a == b == c
true

julia> a == c
false

Comparison involving numbers is intransitive as well:

julia> a = Gain{Unitful.Decibel, :rp}(20) # 20 dB (root-power) == factor 10
20 dB

julia> b = Gain{Unitful.Decibel, :p}(10) # 10 dB (power) == factor 10
10 dB

julia> c = Gain{Unitful.Decibel, :p}(20) # 20 dB (power) == factor 100
20 dB

julia> a == 10 == b
true

julia> a == b
false

julia> 10 == a == c
true

julia> 10 == c
false

To obtain a consistent behavior for ==, the promotion rules for Gain would have to be changed. It might be difficult to figure out a set of rules that is both practical and consistent, unless one gets rid of Gain{L, :?} altogether.

[sostock]

One consequence of the intransitive isequal is that a correct hash implementation for Gain is impossible: We have

• isequal(Gain{Decibel, :p}(20), Gain{Decibel,:rp}(20)),
• isequal(Gain{Decibel, :p}(20), 100), and
• isequal(Gain{Decibel,:rp}(20), 10),

but hash(10) != hash(100).

[kapple19]

Can someone explain why Unitful stores :p or :rp?
Why is it we aren't just storing a logarithmic value along with linear units and logarithmic multiplier it was calculated with, and converting to power or root-power when requested?

Whether a logarithm value was calculated from root-power or power doesn't matter. What matters is that we just choose one to store (say, power) for all logarithmic quantities, and then when the linear quantity is requested, the user specifies if they want power or root-power as the outputted linear quantity.