replace O(n^2) LOC with constant-prop in Dates

[LilithHafner]

julia> using Dates, Base.Order

julia> @code_llvm lt(By(Dates.days ∘ oneunit, Reverse), Week(3), Quarter(2))
;  @ ordering.jl:119 within `lt`
define i8 @julia_lt_9867([1 x i64]* nocapture noundef nonnull readonly align 8 dereferenceable(8) %0, [1 x i64]* nocapture noundef nonnull readonly align 8 dereferenceable(8) %1) #0 {
top:
  ret i8 0
}

[quinnj]

Hmmm, what's going on here? Can you explain the magic?

[LilithHafner]

Sure!

We sort periods in decreasing order (rev = true) according to the length of the period (e.g Week(1) before Hour(240)). There are many ways to get the length of a period p and days(oneunit(p)) seems like a reasonable choice. How many days is one Second/Week/Year? This is sometimes a Flaot64 and sometimes an Int64 but we already don't have type stability because we are working with Vector{Period} and this constant folds once the type is known.

[LilithHafner]

That explanation feels a bit long to include as a comment, but we could if you think it is appropriate.

[gbaraldi]

Yeah adding a comment on how this works is probably a good idea, specially given that the code it replaces is pretty obvious in how it works

[LilithHafner]

Does this explain it adequitely?

# We sort periods in decreasing order (rev = true) according to the length of
# the period's type (by = days ∘ oneunit). We sort by type, not value, so that
# we can merge equal types.
#
# This works by computing how many days are in a single period, and then sorting
# by that. For example, (days ∘ oneunit)(Week(10)) = days(oneunit(Week(10))) =
# days(Week(1)) = 7, which is less than (days ∘ oneunit)(Month(-2)) = 30.436875

[LilithHafner]

Even if this is less obvious, I think its a worthwhile change because it takes the number of new methods to be implemented for a new Period type to support CompundPeriods down from O(n) to 0.

[gbaraldi]

That sounds quite clear 👍

[LilithHafner]

Thanks!