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# This file is a part of Julia. License is MIT: https://julialang.org/license
module Order
import ..@__MODULE__, ..parentmodule
const Base = parentmodule(@__MODULE__)
import .Base:
AbstractVector, @propagate_inbounds, isless, identity, getindex, reverse,
+, -, !, &, <, |
## notions of element ordering ##
export # not exported by Base
Ordering, Forward, Reverse,
By, Lt, Perm,
ReverseOrdering, ForwardOrdering,
DirectOrdering,
lt, ord, ordtype
"""
Base.Order.Ordering
Abstract type which represents a total order on some set of elements.
Use [`Base.Order.lt`](@ref) to compare two elements according to the ordering.
"""
abstract type Ordering end
struct ForwardOrdering <: Ordering end
"""
ReverseOrdering(fwd::Ordering=Forward)
A wrapper which reverses an ordering.
For a given `Ordering` `o`, the following holds for all `a`, `b`:
lt(ReverseOrdering(o), a, b) == lt(o, b, a)
"""
struct ReverseOrdering{Fwd<:Ordering} <: Ordering
fwd::Fwd
end
ReverseOrdering(rev::ReverseOrdering) = rev.fwd
ReverseOrdering(fwd::Fwd) where {Fwd} = ReverseOrdering{Fwd}(fwd)
ReverseOrdering() = ReverseOrdering(ForwardOrdering())
"""
reverse(o::Base.Ordering)
reverses ordering specified by `o`.
"""
reverse(o::Ordering) = ReverseOrdering(o)
const DirectOrdering = Union{ForwardOrdering,ReverseOrdering{ForwardOrdering}}
"""
Base.Order.Forward
Default ordering according to [`isless`](@ref).
"""
const Forward = ForwardOrdering()
"""
Base.Order.Reverse
Reverse ordering according to [`isless`](@ref).
"""
const Reverse = ReverseOrdering()
"""
By(by, order::Ordering=Forward)
`Ordering` which applies `order` to elements after they have been transformed
by the function `by`.
"""
struct By{T, O} <: Ordering
by::T
order::O
end
# backwards compatibility with VERSION < v"1.5-"
By(by) = By(by, Forward)
"""
Lt(lt)
`Ordering` which calls `lt(a, b)` to compare elements. `lt` should
obey the same rules as implementations of [`isless`](@ref).
"""
struct Lt{T} <: Ordering
lt::T
end
"""
Perm(order::Ordering, data::AbstractVector)
`Ordering` on the indices of `data` where `i` is less than `j` if `data[i]` is
less than `data[j]` according to `order`. In the case that `data[i]` and
`data[j]` are equal, `i` and `j` are compared by numeric value.
"""
struct Perm{O<:Ordering,V<:AbstractVector} <: Ordering
order::O
data::V
end
ReverseOrdering(by::By) = By(by.by, ReverseOrdering(by.order))
ReverseOrdering(perm::Perm) = Perm(ReverseOrdering(perm.order), perm.data)
"""
lt(o::Ordering, a, b)
Test whether `a` is less than `b` according to the ordering `o`.
"""
lt(o::ForwardOrdering, a, b) = isless(a,b)
lt(o::ReverseOrdering, a, b) = lt(o.fwd,b,a)
lt(o::By, a, b) = lt(o.order,o.by(a),o.by(b))
lt(o::Lt, a, b) = o.lt(a,b)
@propagate_inbounds function lt(p::Perm, a::Integer, b::Integer)
da = p.data[a]
db = p.data[b]
lt(p.order, da, db) | (!lt(p.order, db, da) & (a < b))
end
_ord(lt::typeof(isless), by::typeof(identity), order::Ordering) = order
_ord(lt::typeof(isless), by, order::Ordering) = By(by, order)
function _ord(lt, by, order::Ordering)
if order === Forward
return Lt((x, y) -> lt(by(x), by(y)))
elseif order === Reverse
return Lt((x, y) -> lt(by(y), by(x)))
else
error("Passing both lt= and order= arguments is ambiguous; please pass order=Forward or order=Reverse (or leave default)")
end
end
"""
ord(lt, by, rev::Union{Bool, Nothing}, order::Ordering=Forward)
Construct an [`Ordering`](@ref) object from the same arguments used by
[`sort!`](@ref).
Elements are first transformed by the function `by` (which may be
[`identity`](@ref)) and are then compared according to either the function `lt`
or an existing ordering `order`. `lt` should be [`isless`](@ref) or a function
which obeys similar rules. Finally, the resulting order is reversed if
`rev=true`.
Passing an `lt` other than `isless` along with an `order` other than
[`Base.Order.Forward`](@ref) or [`Base.Order.Reverse`](@ref) is not permitted,
otherwise all options are independent and can be used together in all possible
combinations.
"""
ord(lt, by, rev::Nothing, order::Ordering=Forward) = _ord(lt, by, order)
function ord(lt, by, rev::Bool, order::Ordering=Forward)
o = _ord(lt, by, order)
return rev ? ReverseOrdering(o) : o
end
# This function is not in use anywhere in Base but we observed
# use in sorting-related packages (#34719). It's probably best to move
# this functionality to those packages in the future; let's remind/force
# ourselves to deprecate this in v2.0.
# The following clause means `if VERSION < v"2.0-"` but it also works during
# bootstrap. For the same reason, we need to write `Int32` instead of `Cint`.
if ccall(:jl_ver_major, Int32, ()) < 2
ordtype(o::ReverseOrdering, vs::AbstractArray) = ordtype(o.fwd, vs)
ordtype(o::Perm, vs::AbstractArray) = ordtype(o.order, o.data)
# TODO: here, we really want the return type of o.by, without calling it
ordtype(o::By, vs::AbstractArray) = try typeof(o.by(vs[1])) catch; Any end
ordtype(o::Ordering, vs::AbstractArray) = eltype(vs)
end
end
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