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support sorting tuples
Uses merge sort, as an obvious choice for a stable sort of tuples. A recursive data structure of singleton type, representing Peano natural numbers, is used to help with splitting a tuple into two halves in the merge sort. An alternative design would use a reference tuple, but this would require relying on `tail`, which seems more harsh on the compiler. With the recursive datastructure the predecessor operation and the successor operation are both trivial. Allows inference to preserve inferred element type even when tuple length is not known. Follow-up PRs may add further improvements, such as the ability to select an unstable sorting algorithm. The added file, typedomainnumbers.jl is not specific to sorting, thus making it a separate file. Xref JuliaLang#55571. Fixes JuliaLang#54489
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‎NEWS.md

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@@ -119,6 +119,7 @@ New library features
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* `Base.require_one_based_indexing` and `Base.has_offset_axes` are now public ([#56196])
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* New `ltruncate`, `rtruncate` and `ctruncate` functions for truncating strings to text width, accounting for char widths ([#55351])
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* `isless` (and thus `cmp`, sorting, etc.) is now supported for zero-dimensional `AbstractArray`s ([#55772])
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* `sort` now sorts tuples (#56425)
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Standard library changes
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------------------------

‎base/Base.jl

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@@ -106,6 +106,8 @@ include("cartesian.jl")
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using .Cartesian
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include("multidimensional.jl")
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include("typedomainnumbers.jl")
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include("broadcast.jl")
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using .Broadcast
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using .Broadcast: broadcasted, broadcasted_kwsyntax, materialize, materialize!,

‎base/sort.jl

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@@ -1736,6 +1736,95 @@ julia> v
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"""
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sort(v::AbstractVector; kws...) = sort!(copymutable(v); kws...)
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module _SortTupleStable
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using
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Base._TypeDomainNumbers.PositiveIntegers, Base._TypeDomainNumbers.IntegersGreaterThanOne,
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Base._TypeDomainNumbers.Utils, Base._TypeDomainNumberTupleUtils, Base._TupleTypeByLength
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using Base: tail
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using Base.Order: Ordering, lt
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export sort_tuple_stable
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function merge_recursive((@nospecialize ord::Ordering), a::Tuple, b::Tuple)
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ret = if a isa Tuple1OrMore
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a
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else
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b
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end
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type_assert_tuple_0_or_more(ret)
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end
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function merge_recursive(ord::Ordering, a::Tuple1OrMore, b::Tuple1OrMore)
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l = first(a)
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r = first(b)
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x = tail(a)
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y = tail(b)
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merged = if lt(ord, r, l)
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let rec = type_assert_tuple_1_or_more(merge_recursive(ord, a, y))
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(r, rec...)
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end
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else
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let rec = type_assert_tuple_1_or_more(merge_recursive(ord, x, b))
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(l, rec...)
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end
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end
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type_assert_tuple_2_or_more(merged)
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end
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function merge_nontrivial(ord::Ordering, a::Tuple1OrMore, b::Tuple1OrMore)
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ret = merge_recursive(ord, a, b)
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type_assert_tuple_2_or_more(ret)
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end
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function split_tuple(@nospecialize tup::Tuple2OrMore)
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len = type_assert_integer_greater_than_1(tuple_type_domain_length(tup))
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len_l = type_assert_positive_integer(half_floor_nontrivial(len))
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len_r = type_assert_positive_integer(half_ceiling_nontrivial(len))
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tup_l = type_assert_tuple_1_or_more(skip_from_tail_nontrivial(tup, len_r))
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tup_r = type_assert_tuple_1_or_more(skip_from_front_nontrivial(tup, len_l))
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(tup_l, tup_r)
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end
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function sort_recursive((@nospecialize ord::Ordering), @nospecialize tup::Tuple{Any})
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tup
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end
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function sort_recursive(ord::Ordering, tup::Tuple2OrMore)
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(tup_l, tup_r) = split_tuple(tup)
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sorted_l = type_assert_tuple_1_or_more(sort_recursive(ord, tup_l))
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sorted_r = type_assert_tuple_1_or_more(sort_recursive(ord, tup_r))
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type_assert_tuple_2_or_more(merge_nontrivial(ord, sorted_l, sorted_r))
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end
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function sort_tuple_stable_2_or_more(ord::Ordering, tup::Tuple2OrMore)
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ret = sort_recursive(ord, tup)
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type_assert_tuple_2_or_more(ret)
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end
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function sort_tuple_array_fallback(ord::Ordering, tup::Tuple2OrMore)
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vec = if tup isa NTuple
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[tup...]
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else
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Any[tup...]
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end
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sort!(vec; order = ord)
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(vec...,)
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end
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function sort_tuple_stable((@nospecialize ord::Ordering), @nospecialize tup::Tuple)
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if tup isa Tuple2OrMore
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if tup isa Tuple32OrMore
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sort_tuple_array_fallback(ord, tup)
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else
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sort_tuple_stable_2_or_more(ord, tup)
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end
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else
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tup
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end
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end
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end
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function sort(
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tup::Tuple;
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lt = isless,
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by = identity,
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rev::Union{Nothing, Bool} = nothing,
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order::Ordering = Forward,
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)
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o = ord(lt, by, rev, order)
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_SortTupleStable.sort_tuple_stable(o, tup)
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end
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## partialsortperm: the permutation to sort the first k elements of an array ##
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"""

‎base/typedomainnumbers.jl

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# This file is a part of Julia. License is MIT: https://julialang.org/license
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# Adapted from the TypeDomainNaturalNumbers.jl package.
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module _TypeDomainNumbers
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module Zeros
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export Zero
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struct Zero end
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end
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module PositiveIntegers
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module RecursiveStep
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using ...Zeros
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export recursive_step
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function recursive_step(@nospecialize t::Type)
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Union{Zero, t}
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end
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end
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module UpperBounds
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using ..RecursiveStep
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abstract type A end
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abstract type B{P <: recursive_step(A)} <: A end
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abstract type C{P <: recursive_step(B)} <: B{P} end
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abstract type D{P <: recursive_step(C)} <: C{P} end
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end
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using .RecursiveStep
26+
const PositiveIntegerUpperBound = UpperBounds.A
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const PositiveIntegerUpperBoundTighter = UpperBounds.D
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export
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natural_successor, natural_predecessor,
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NonnegativeInteger, NonnegativeIntegerUpperBound,
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PositiveInteger, PositiveIntegerUpperBound,
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type_assert_nonnegative_integer, type_assert_positive_integer
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struct PositiveInteger{
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Predecessor <: recursive_step(PositiveIntegerUpperBoundTighter),
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} <: PositiveIntegerUpperBoundTighter{Predecessor}
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predecessor::Predecessor
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global const NonnegativeInteger = recursive_step(PositiveInteger)
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global const NonnegativeIntegerUpperBound = recursive_step(PositiveIntegerUpperBound)
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global function natural_successor(p::P) where {P <: NonnegativeInteger}
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ret = new{P}(p)
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type_assert_positive_integer(ret)
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end
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end
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function type_assert_nonnegative_integer(@nospecialize x::NonnegativeInteger)
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x
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end
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function type_assert_positive_integer(@nospecialize x::PositiveInteger)
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x
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end
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function natural_predecessor(@nospecialize o::PositiveInteger)
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ret = getfield(o, :predecessor) # avoid specializing `getproperty` for each number
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type_assert_nonnegative_integer(ret)
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end
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end
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module IntegersGreaterThanOne
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using ..PositiveIntegers
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export
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IntegerGreaterThanOne, IntegerGreaterThanOneUpperBound,
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type_assert_integer_greater_than_1
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const IntegerGreaterThanOne = let t = PositiveInteger
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t{P} where {P <: t}
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end
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const IntegerGreaterThanOneUpperBound = let t = PositiveIntegerUpperBound
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PositiveIntegers.UpperBounds.B{P} where {P <: t}
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end
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function type_assert_integer_greater_than_1(@nospecialize x::IntegerGreaterThanOne)
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x
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end
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end
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module Constants
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using ..Zeros, ..PositiveIntegers
74+
export n0, n1
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const n0 = Zero()
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const n1 = natural_successor(n0)
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end
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79+
module Utils
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using ..PositiveIntegers, ..IntegersGreaterThanOne, ..Constants
81+
using Base: @assume_effects
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export minus_two, half_floor, half_ceiling, half_floor_nontrivial, half_ceiling_nontrivial
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function minus_two(@nospecialize m::IntegerGreaterThanOne)
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natural_predecessor(natural_predecessor(m))
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end
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@assume_effects :foldable :nothrow function half_floor(@nospecialize m::NonnegativeInteger)
87+
ret = if m isa IntegerGreaterThanOneUpperBound
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let n = minus_two(m), rec = half_floor(n)
89+
type_assert_positive_integer(natural_successor(rec))
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end
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else
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n0
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end
94+
type_assert_nonnegative_integer(ret)
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end
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@assume_effects :foldable :nothrow function half_ceiling(@nospecialize m::NonnegativeInteger)
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ret = if m isa IntegerGreaterThanOneUpperBound
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let n = minus_two(m), rec = half_ceiling(n)
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type_assert_positive_integer(natural_successor(rec))
100+
end
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else
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if m isa PositiveIntegerUpperBound
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n1
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else
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n0
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end
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end
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type_assert_nonnegative_integer(ret)
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end
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function half_floor_nontrivial(@nospecialize m::IntegerGreaterThanOne)
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ret = half_floor(m)
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type_assert_positive_integer(ret)
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end
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function half_ceiling_nontrivial(@nospecialize m::IntegerGreaterThanOne)
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ret = half_ceiling(m)
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type_assert_positive_integer(ret)
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end
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end
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end
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module _TupleTypeByLength
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export
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Tuple1OrMore, Tuple2OrMore, Tuple3OrMore, Tuple4OrMore, Tuple32OrMore,
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type_assert_tuple_0_or_more, type_assert_tuple_1_or_more, type_assert_tuple_2_or_more,
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type_assert_tuple_3_or_more, type_assert_tuple_4_or_more,
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type_assert_tuple_1
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const Tuple1OrMore = Tuple{Any, Vararg}
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const Tuple2OrMore = Tuple{Any, Any, Vararg}
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const Tuple3OrMore = Tuple{Any, Any, Any, Vararg}
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const Tuple4OrMore = Tuple{Any, Any, Any, Any, Vararg}
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const Tuple32OrMore = Base.Any32
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function type_assert_tuple_0_or_more(@nospecialize x::Tuple)
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x
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end
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function type_assert_tuple_1_or_more(@nospecialize x::Tuple1OrMore)
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x
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end
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function type_assert_tuple_2_or_more(@nospecialize x::Tuple2OrMore)
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x
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end
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function type_assert_tuple_3_or_more(@nospecialize x::Tuple3OrMore)
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x
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end
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function type_assert_tuple_4_or_more(@nospecialize x::Tuple4OrMore)
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x
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end
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end
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module _TypeDomainNumberTupleUtils
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using
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.._TypeDomainNumbers.PositiveIntegers, .._TypeDomainNumbers.IntegersGreaterThanOne,
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.._TypeDomainNumbers.Constants, .._TupleTypeByLength
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using Base: @assume_effects, front, tail
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export
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tuple_type_domain_length,
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skip_from_front, skip_from_tail,
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skip_from_front_nontrivial, skip_from_tail_nontrivial
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# The `@nospecialize` and `@inline` together should effectively result in specializing
159+
# on the length, without specializing on the types of the elements.
160+
@assume_effects :foldable :nothrow function tuple_type_domain_length(@nospecialize tup::Tuple)
161+
ret = if tup isa Tuple1OrMore
162+
let t = tail(tup), rec = @inline tuple_type_domain_length(t)
163+
type_assert_positive_integer(natural_successor(rec))
164+
end
165+
else
166+
n0
167+
end
168+
type_assert_nonnegative_integer(ret)
169+
end
170+
@assume_effects :foldable function skip_from_front((@nospecialize tup::Tuple), @nospecialize skip_count::NonnegativeInteger)
171+
if skip_count isa PositiveIntegerUpperBound
172+
let cm1 = natural_predecessor(skip_count), t = tail(tup)
173+
@inline skip_from_front(t, cm1)
174+
end
175+
else
176+
tup
177+
end
178+
end
179+
@assume_effects :foldable function skip_from_tail((@nospecialize tup::Tuple), @nospecialize skip_count::NonnegativeInteger)
180+
if skip_count isa PositiveIntegerUpperBound
181+
let cm1 = natural_predecessor(skip_count), t = front(tup)
182+
@inline skip_from_tail(t, cm1)
183+
end
184+
else
185+
tup
186+
end
187+
end
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function skip_from_front_nontrivial((@nospecialize tup::Tuple2OrMore), @nospecialize skip_count::PositiveInteger)
189+
skip_from_front(tup, skip_count)
190+
end
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function skip_from_tail_nontrivial((@nospecialize tup::Tuple2OrMore), @nospecialize skip_count::PositiveInteger)
192+
skip_from_tail(tup, skip_count)
193+
end
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end

‎test/sorting.jl

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end
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@test sort(1:2000, by=x->x÷100, rev=true) == sort(1:2000, by=x->-x÷100) ==
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vcat(2000, (x:x+99 for x in 1900:-100:100)..., 1:99)
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@testset "tuples" begin
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tup = Tuple(0:9)
97+
@test tup === sort(tup; by = _ -> 0)
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@test (0, 2, 4, 6, 8, 1, 3, 5, 7, 9) === sort(tup; by = x -> isodd(x))
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@test (1, 3, 5, 7, 9, 0, 2, 4, 6, 8) === sort(tup; by = x -> iseven(x))
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end
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end
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103+
@testset "tuple sorting" begin
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max_unrolled_length = 31
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@testset "correctness" begin
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tup = Tuple(0:9)
107+
tup_rev = reverse(tup)
108+
@test tup === @inferred sort(tup)
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@test tup === sort(tup; rev = false)
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@test tup_rev === sort(tup; rev = true)
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@test tup_rev === sort(tup; lt = >)
112+
end
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@testset "inference" begin
114+
known_length = (Tuple{Vararg{Int, max_unrolled_length}}, Tuple{Vararg{Float64, max_unrolled_length}})
115+
unknown_length = (Tuple{Vararg{Int}}, Tuple{Vararg{Float64}})
116+
for Tup ∈ (known_length..., unknown_length...)
117+
@test Tup == Base.infer_return_type(sort, Tuple{Tup})
118+
end
119+
for Tup ∈ (known_length...,)
120+
@test Core.Compiler.is_foldable(Base.infer_effects(sort, Tuple{Tup}))
121+
end
122+
end
123+
@testset "alloc" begin
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function test_zero_allocated(tup::Tuple)
125+
@test iszero(@allocated sort(tup))
126+
end
127+
test_zero_allocated(ntuple(identity, max_unrolled_length))
128+
end
129+
@testset "heterogeneous" begin
130+
@testset "stability" begin
131+
tup = (0, 0x0, 0x000)
132+
@test tup === sort(tup)
133+
end
134+
tup = (1, 2, 3, missing, missing)
135+
for t ∈ (tup, (1, missing, 2, missing, 3), (missing, missing, 1, 2, 3))
136+
@test tup === @inferred sort(t)
137+
end
138+
end
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end
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@testset "partialsort" begin

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